<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When Erick went to the market to sell his fruits, he realized that the price of lemons had risen by $4 for each lemon. The price of grapes had also increased by half the price that the price of lemon increased by per grape. He had planned to sell the lemons at $8 and the grapes at $7, and he had 80 lemons and some number of grapes in his basket. He collected $2220 from selling the fruits at the new prices. How many grapes did he have in his basket?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When Erick went to the market to sell his fruits, he realized that the price of lemons had risen by $4 for each lemon. The price of grapes had also increased by half the price that the price of lemon increased by per grape. He had planned to sell the lemons at $8 and the grapes at $7, and he had 80 lemons and some number of grapes in his basket. He collected $2220 from selling the fruits at the new prices. How many grapes did he have in his basket?<|im_end|>
<|im_start|>assistant
<Z_104><Z_63><Z_30><Z_40><Z_32><Z_40><Z_117><Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When Erick went to the market to sell his fruits, he realized that the price of lemons had risen by $4 for each lemon. The price of grapes had also increased by half the price that the price of lemon increased by per grape. He had planned to sell the lemons at $8 and the grapes at $7, and he had 80 lemons and some number of grapes in his basket. He collected $2220 from selling the fruits at the new prices. How many grapes did he have in his basket?<|im_end|>
<|im_start|>assistant
<Z_98><Z_49><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When Erick went to the market to sell his fruits, he realized that the price of lemons had risen by $4 for each lemon. The price of grapes had also increased by half the price that the price of lemon increased by per grape. He had planned to sell the lemons at $8 and the grapes at $7, and he had 80 lemons and some number of grapes in his basket. He collected $2220 from selling the fruits at the new prices. How many grapes did he have in his basket?<|im_end|>
<|im_start|>assistant
<Z_41><Z_55><Z_98><Z_51><Z_11><Z_85><Z_31><Z_96><ANSWER>

Question: When Erick went to the market to sell his fruits, he realized that the price of lemons had risen by $4 for each lemon. The price of grapes had also increased by half the price that the price of lemon increased by per grape. He had planned to sell the lemons at $8 and the grapes at $7, and he had 80 lemons and some number of grapes in his basket. He collected $2220 from selling the fruits at the new prices. How many grapes did he have in his basket?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is an unlimited supply of congruent equilateral triangles made of colored paper. Each triangle is a solid color with the same color on both sides of the paper. A large equilateral triangle is constructed from four of these paper triangles. Two large triangles are considered distinguishable if it is not possible to place one on the other, using translations, rotations, and/or reflections, so that their corresponding small triangles are of the same color. Given that there are eight different colors of triangles from which to choose, and the center triangle must not be red, how many distinguishable large equilateral triangles can be constructed?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is an unlimited supply of congruent equilateral triangles made of colored paper. Each triangle is a solid color with the same color on both sides of the paper. A large equilateral triangle is constructed from four of these paper triangles. Two large triangles are considered distinguishable if it is not possible to place one on the other, using translations, rotations, and/or reflections, so that their corresponding small triangles are of the same color. Given that there are eight different colors of triangles from which to choose, and the center triangle must not be red, how many distinguishable large equilateral triangles can be constructed?<|im_end|>
<|im_start|>assistant
<Z_113><Z_43><Z_78><Z_81><Z_78><Z_49><Z_80><Z_124><Z_78><Z_12><Z_39><Z_124><Z_45><Z_76><Z_26><Z_10><Z_98><Z_58><Z_98><Z_52><Z_45><Z_47><Z_54><Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is an unlimited supply of congruent equilateral triangles made of colored paper. Each triangle is a solid color with the same color on both sides of the paper. A large equilateral triangle is constructed from four of these paper triangles. Two large triangles are considered distinguishable if it is not possible to place one on the other, using translations, rotations, and/or reflections, so that their corresponding small triangles are of the same color. Given that there are eight different colors of triangles from which to choose, and the center triangle must not be red, how many distinguishable large equilateral triangles can be constructed?<|im_end|>
<|im_start|>assistant
<Z_98><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There is an unlimited supply of congruent equilateral triangles made of colored paper. Each triangle is a solid color with the same color on both sides of the paper. A large equilateral triangle is constructed from four of these paper triangles. Two large triangles are considered distinguishable if it is not possible to place one on the other, using translations, rotations, and/or reflections, so that their corresponding small triangles are of the same color. Given that there are eight different colors of triangles from which to choose, and the center triangle must not be red, how many distinguishable large equilateral triangles can be constructed?<|im_end|>
<|im_start|>assistant
<Z_64><Z_93><Z_90><Z_23><Z_106><Z_70><Z_63><Z_3><Z_78><Z_4><Z_31><Z_56><Z_75><Z_69><Z_96><Z_58><Z_51><Z_10><Z_34><Z_80><Z_5><Z_14><Z_15><Z_80><ANSWER>

Question: There is an unlimited supply of congruent equilateral triangles made of colored paper. Each triangle is a solid color with the same color on both sides of the paper. A large equilateral triangle is constructed from four of these paper triangles. Two large triangles are considered distinguishable if it is not possible to place one on the other, using translations, rotations, and/or reflections, so that their corresponding small triangles are of the same color. Given that there are eight different colors of triangles from which to choose, and the center triangle must not be red, how many distinguishable large equilateral triangles can be constructed?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 2000 feet high and bounces back up two-thirds of the distance it just fell. After how many bounces will the ball first reach a maximum height less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 2000 feet high and bounces back up two-thirds of the distance it just fell. After how many bounces will the ball first reach a maximum height less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_94><Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 2000 feet high and bounces back up two-thirds of the distance it just fell. After how many bounces will the ball first reach a maximum height less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_18><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A ball is dropped from 2000 feet high and bounces back up two-thirds of the distance it just fell. After how many bounces will the ball first reach a maximum height less than 2 feet?<|im_end|>
<|im_start|>assistant
<Z_127><Z_40><ANSWER>

Question: A ball is dropped from 2000 feet high and bounces back up two-thirds of the distance it just fell. After how many bounces will the ball first reach a maximum height less than 2 feet?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Michel starts with the string \( H M M T \). An operation consists of either replacing an occurrence of \( H \) with \( H M \), replacing an occurrence of \( M M \) with \( M O M \), or replacing an occurrence of \( T \) with \( M T \). For example, the two strings that can be reached after one operation are \( H M M M T \) and \( H M O M T \). Compute the number of distinct strings Michel can obtain after exactly 10 operations.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Michel starts with the string \( H M M T \). An operation consists of either replacing an occurrence of \( H \) with \( H M \), replacing an occurrence of \( M M \) with \( M O M \), or replacing an occurrence of \( T \) with \( M T \). For example, the two strings that can be reached after one operation are \( H M M M T \) and \( H M O M T \). Compute the number of distinct strings Michel can obtain after exactly 10 operations.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Michel starts with the string \( H M M T \). An operation consists of either replacing an occurrence of \( H \) with \( H M \), replacing an occurrence of \( M M \) with \( M O M \), or replacing an occurrence of \( T \) with \( M T \). For example, the two strings that can be reached after one operation are \( H M M M T \) and \( H M O M T \). Compute the number of distinct strings Michel can obtain after exactly 10 operations.<|im_end|>
<|im_start|>assistant
<Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Michel starts with the string \( H M M T \). An operation consists of either replacing an occurrence of \( H \) with \( H M \), replacing an occurrence of \( M M \) with \( M O M \), or replacing an occurrence of \( T \) with \( M T \). For example, the two strings that can be reached after one operation are \( H M M M T \) and \( H M O M T \). Compute the number of distinct strings Michel can obtain after exactly 10 operations.<|im_end|>
<|im_start|>assistant
<Z_84><ANSWER>

Question: Michel starts with the string \( H M M T \). An operation consists of either replacing an occurrence of \( H \) with \( H M \), replacing an occurrence of \( M M \) with \( M O M \), or replacing an occurrence of \( T \) with \( M T \). For example, the two strings that can be reached after one operation are \( H M M M T \) and \( H M O M T \). Compute the number of distinct strings Michel can obtain after exactly 10 operations.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tom had 27 pennies and 15 dimes in his bank. His dad gave him 33 dimes and 49 nickels. How many dimes does he have now?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tom had 27 pennies and 15 dimes in his bank. His dad gave him 33 dimes and 49 nickels. How many dimes does he have now?<|im_end|>
<|im_start|>assistant
<Z_104><Z_58><Z_43><Z_49><Z_125><Z_58><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tom had 27 pennies and 15 dimes in his bank. His dad gave him 33 dimes and 49 nickels. How many dimes does he have now?<|im_end|>
<|im_start|>assistant
<Z_23><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tom had 27 pennies and 15 dimes in his bank. His dad gave him 33 dimes and 49 nickels. How many dimes does he have now?<|im_end|>
<|im_start|>assistant
<Z_46><Z_15><Z_105><Z_74><Z_85><Z_23><Z_4><ANSWER>

Question: Tom had 27 pennies and 15 dimes in his bank. His dad gave him 33 dimes and 49 nickels. How many dimes does he have now?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marla is mixing a particular shade of lilac that's 70% blue paint, 20% red paint, and the rest white paint. She adds a certain amount of blue paint and 20 ounces of white paint. If the blue paint makes up 70% of the mixture, how many ounces of blue paint does she add?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marla is mixing a particular shade of lilac that's 70% blue paint, 20% red paint, and the rest white paint. She adds a certain amount of blue paint and 20 ounces of white paint. If the blue paint makes up 70% of the mixture, how many ounces of blue paint does she add?<|im_end|>
<|im_start|>assistant
<Z_113><Z_47><Z_115><Z_101><Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marla is mixing a particular shade of lilac that's 70% blue paint, 20% red paint, and the rest white paint. She adds a certain amount of blue paint and 20 ounces of white paint. If the blue paint makes up 70% of the mixture, how many ounces of blue paint does she add?<|im_end|>
<|im_start|>assistant
<Z_75><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marla is mixing a particular shade of lilac that's 70% blue paint, 20% red paint, and the rest white paint. She adds a certain amount of blue paint and 20 ounces of white paint. If the blue paint makes up 70% of the mixture, how many ounces of blue paint does she add?<|im_end|>
<|im_start|>assistant
<Z_107><Z_124><Z_91><Z_54><Z_81><ANSWER>

Question: Marla is mixing a particular shade of lilac that's 70% blue paint, 20% red paint, and the rest white paint. She adds a certain amount of blue paint and 20 ounces of white paint. If the blue paint makes up 70% of the mixture, how many ounces of blue paint does she add?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jonsey is awake for 2/3 of the day and spends 1/2 her time awake playing outside and the rest inside. Her brother, Riley, is awake for 3/4 of the day and spends 1/3 of his day outside and the rest inside. How much time, on average, do they spend inside?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jonsey is awake for 2/3 of the day and spends 1/2 her time awake playing outside and the rest inside. Her brother, Riley, is awake for 3/4 of the day and spends 1/3 of his day outside and the rest inside. How much time, on average, do they spend inside?<|im_end|>
<|im_start|>assistant
<Z_104><Z_87><Z_80><Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jonsey is awake for 2/3 of the day and spends 1/2 her time awake playing outside and the rest inside. Her brother, Riley, is awake for 3/4 of the day and spends 1/3 of his day outside and the rest inside. How much time, on average, do they spend inside?<|im_end|>
<|im_start|>assistant
<Z_11><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Jonsey is awake for 2/3 of the day and spends 1/2 her time awake playing outside and the rest inside. Her brother, Riley, is awake for 3/4 of the day and spends 1/3 of his day outside and the rest inside. How much time, on average, do they spend inside?<|im_end|>
<|im_start|>assistant
<Z_106><Z_127><Z_35><Z_3><ANSWER>

Question: Jonsey is awake for 2/3 of the day and spends 1/2 her time awake playing outside and the rest inside. Her brother, Riley, is awake for 3/4 of the day and spends 1/3 of his day outside and the rest inside. How much time, on average, do they spend inside?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A woman purchased 3 towels at Rs. 100 each, 5 towels at Rs. 150 each, and two towels at a certain rate which is now slipped off from her memory. She remembers that the average price of the towels was Rs. 165. What was the unknown rate of the two towels?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A woman purchased 3 towels at Rs. 100 each, 5 towels at Rs. 150 each, and two towels at a certain rate which is now slipped off from her memory. She remembers that the average price of the towels was Rs. 165. What was the unknown rate of the two towels?<|im_end|>
<|im_start|>assistant
<Z_106><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A woman purchased 3 towels at Rs. 100 each, 5 towels at Rs. 150 each, and two towels at a certain rate which is now slipped off from her memory. She remembers that the average price of the towels was Rs. 165. What was the unknown rate of the two towels?<|im_end|>
<|im_start|>assistant
<Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A woman purchased 3 towels at Rs. 100 each, 5 towels at Rs. 150 each, and two towels at a certain rate which is now slipped off from her memory. She remembers that the average price of the towels was Rs. 165. What was the unknown rate of the two towels?<|im_end|>
<|im_start|>assistant
<Z_89><ANSWER>

Question: A woman purchased 3 towels at Rs. 100 each, 5 towels at Rs. 150 each, and two towels at a certain rate which is now slipped off from her memory. She remembers that the average price of the towels was Rs. 165. What was the unknown rate of the two towels?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $b_n$ be the number obtained by writing the integers 1 to $n$ from left to right in reverse order. For example, $b_4 = 4321$ and $b_{12} = 121110987654321$. For $1 \le k \le 150$, how many $b_k$ are divisible by 9?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $b_n$ be the number obtained by writing the integers 1 to $n$ from left to right in reverse order. For example, $b_4 = 4321$ and $b_{12} = 121110987654321$. For $1 \le k \le 150$, how many $b_k$ are divisible by 9?<|im_end|>
<|im_start|>assistant
<Z_104><Z_4><Z_89><Z_87><Z_73><Z_82><Z_95><Z_56><Z_63><Z_38><Z_70><Z_58><Z_31><Z_39><Z_39><Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let $b_n$ be the number obtained by writing the integers 1 to $n$ from left to right in reverse order. For example, $b_4 = 4321$ and $b_{12} = 121110987654321$. For $1 \le k \le 150$, how many $b_k$ are divisible by 9?<|im_end|>
<|im_start|>assistant
<Z_8><Z_17><Z_95><Z_50><Z_126><Z_28><Z_114><Z_127><Z_49><Z_63><Z_9><Z_105><Z_32><Z_15><Z_92><Z_46><ANSWER>

Question: Let $b_n$ be the number obtained by writing the integers 1 to $n$ from left to right in reverse order. For example, $b_4 = 4321$ and $b_{12} = 121110987654321$. For $1 \le k \le 150$, how many $b_k$ are divisible by 9?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes a dog groomer 10 minutes to dry a short-haired dog like a beagle. It takes him twice as long to dry a full-haired, fluffy dog like a german shepherd. One morning, he has 6 short-haired dogs to dry and 9 full-haired dogs to dry. How many hours does it take him to dry all of the dogs?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes a dog groomer 10 minutes to dry a short-haired dog like a beagle. It takes him twice as long to dry a full-haired, fluffy dog like a german shepherd. One morning, he has 6 short-haired dogs to dry and 9 full-haired dogs to dry. How many hours does it take him to dry all of the dogs?<|im_end|>
<|im_start|>assistant
<Z_57><Z_100><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes a dog groomer 10 minutes to dry a short-haired dog like a beagle. It takes him twice as long to dry a full-haired, fluffy dog like a german shepherd. One morning, he has 6 short-haired dogs to dry and 9 full-haired dogs to dry. How many hours does it take him to dry all of the dogs?<|im_end|>
<|im_start|>assistant
<Z_110><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
It takes a dog groomer 10 minutes to dry a short-haired dog like a beagle. It takes him twice as long to dry a full-haired, fluffy dog like a german shepherd. One morning, he has 6 short-haired dogs to dry and 9 full-haired dogs to dry. How many hours does it take him to dry all of the dogs?<|im_end|>
<|im_start|>assistant
<Z_87><Z_26><ANSWER>

Question: It takes a dog groomer 10 minutes to dry a short-haired dog like a beagle. It takes him twice as long to dry a full-haired, fluffy dog like a german shepherd. One morning, he has 6 short-haired dogs to dry and 9 full-haired dogs to dry. How many hours does it take him to dry all of the dogs?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $\frac{1}{3}\cdot\frac{9}{1}\cdot\frac{1}{27}\cdot\frac{81}{1} \dotsm \frac{1}{2187}\cdot\frac{6561}{1}$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $\frac{1}{3}\cdot\frac{9}{1}\cdot\frac{1}{27}\cdot\frac{81}{1} \dotsm \frac{1}{2187}\cdot\frac{6561}{1}$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_64><Z_64><Z_30><Z_59><Z_96><Z_124><Z_56><Z_63><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $\frac{1}{3}\cdot\frac{9}{1}\cdot\frac{1}{27}\cdot\frac{81}{1} \dotsm \frac{1}{2187}\cdot\frac{6561}{1}$?<|im_end|>
<|im_start|>assistant
<Z_22><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of $\frac{1}{3}\cdot\frac{9}{1}\cdot\frac{1}{27}\cdot\frac{81}{1} \dotsm \frac{1}{2187}\cdot\frac{6561}{1}$?<|im_end|>
<|im_start|>assistant
<Z_82><Z_70><Z_43><Z_69><Z_73><Z_126><Z_30><Z_36><Z_82><ANSWER>

Question: What is the value of $\frac{1}{3}\cdot\frac{9}{1}\cdot\frac{1}{27}\cdot\frac{81}{1} \dotsm \frac{1}{2187}\cdot\frac{6561}{1}$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam bought some boxes of chocolate candy and gave 7 to his little brother. Each box has 6 pieces inside it. Adam still has 36 pieces. How many boxes did Adam buy initially?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam bought some boxes of chocolate candy and gave 7 to his little brother. Each box has 6 pieces inside it. Adam still has 36 pieces. How many boxes did Adam buy initially?<|im_end|>
<|im_start|>assistant
<Z_104><Z_114><Z_40><Z_73><Z_99><Z_87><Z_12><Z_82><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam bought some boxes of chocolate candy and gave 7 to his little brother. Each box has 6 pieces inside it. Adam still has 36 pieces. How many boxes did Adam buy initially?<|im_end|>
<|im_start|>assistant
<Z_73><Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam bought some boxes of chocolate candy and gave 7 to his little brother. Each box has 6 pieces inside it. Adam still has 36 pieces. How many boxes did Adam buy initially?<|im_end|>
<|im_start|>assistant
<Z_5><Z_28><Z_121><Z_5><Z_60><Z_72><Z_65><Z_1><Z_75><ANSWER>

Question: Adam bought some boxes of chocolate candy and gave 7 to his little brother. Each box has 6 pieces inside it. Adam still has 36 pieces. How many boxes did Adam buy initially?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ satisfies $f(4x-2) = x^2 - x + 2$ for all real numbers $x$. Determine $f(6)$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ satisfies $f(4x-2) = x^2 - x + 2$ for all real numbers $x$. Determine $f(6)$.<|im_end|>
<|im_start|>assistant
<Z_113><Z_65><Z_72><Z_100><Z_80><Z_37><Z_99><Z_124><Z_93><Z_63><Z_90><Z_76><Z_66><Z_54><Z_82><Z_59><Z_70><Z_83><Z_81><Z_119><Z_9><Z_81><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ satisfies $f(4x-2) = x^2 - x + 2$ for all real numbers $x$. Determine $f(6)$.<|im_end|>
<|im_start|>assistant
<Z_109><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A function $f$ satisfies $f(4x-2) = x^2 - x + 2$ for all real numbers $x$. Determine $f(6)$.<|im_end|>
<|im_start|>assistant
<Z_87><Z_121><Z_22><Z_54><Z_55><Z_10><Z_109><Z_47><Z_79><Z_21><Z_24><Z_84><Z_57><Z_19><Z_124><Z_0><Z_20><Z_105><Z_16><Z_66><Z_124><Z_98><ANSWER>

Question: A function $f$ satisfies $f(4x-2) = x^2 - x + 2$ for all real numbers $x$. Determine $f(6)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Beth had 150 students in her 10th-grade class. The following year, some more students join. In her final year, 15 students left. Beth had 165 students in her class at the end of her final year. How many students joined her class in the following year?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Beth had 150 students in her 10th-grade class. The following year, some more students join. In her final year, 15 students left. Beth had 165 students in her class at the end of her final year. How many students joined her class in the following year?<|im_end|>
<|im_start|>assistant
<Z_94><Z_79><Z_58><Z_63><Z_37><Z_16><Z_49><Z_101><Z_98><Z_16><Z_47><Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Beth had 150 students in her 10th-grade class. The following year, some more students join. In her final year, 15 students left. Beth had 165 students in her class at the end of her final year. How many students joined her class in the following year?<|im_end|>
<|im_start|>assistant
<Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Beth had 150 students in her 10th-grade class. The following year, some more students join. In her final year, 15 students left. Beth had 165 students in her class at the end of her final year. How many students joined her class in the following year?<|im_end|>
<|im_start|>assistant
<Z_4><Z_77><Z_80><Z_66><Z_3><Z_111><Z_27><Z_52><Z_34><Z_3><Z_104><Z_94><ANSWER>

Question: Beth had 150 students in her 10th-grade class. The following year, some more students join. In her final year, 15 students left. Beth had 165 students in her class at the end of her final year. How many students joined her class in the following year?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Observe the following equations: $a+b=1$, $a^{2}+b^{2}=3$, $a^{3}+b^{3}=4$, $a^{4}+b^{4}=7$, $a^{5}+b^{5}=11$, ..., and so on. What is the value of $a^{n}+b^{n}$ when $n=11$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Observe the following equations: $a+b=1$, $a^{2}+b^{2}=3$, $a^{3}+b^{3}=4$, $a^{4}+b^{4}=7$, $a^{5}+b^{5}=11$, ..., and so on. What is the value of $a^{n}+b^{n}$ when $n=11$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_40><Z_58><Z_47><Z_66><Z_37><Z_123><Z_37><Z_63><Z_96><Z_53><Z_115><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Observe the following equations: $a+b=1$, $a^{2}+b^{2}=3$, $a^{3}+b^{3}=4$, $a^{4}+b^{4}=7$, $a^{5}+b^{5}=11$, ..., and so on. What is the value of $a^{n}+b^{n}$ when $n=11$?<|im_end|>
<|im_start|>assistant
<Z_122><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Observe the following equations: $a+b=1$, $a^{2}+b^{2}=3$, $a^{3}+b^{3}=4$, $a^{4}+b^{4}=7$, $a^{5}+b^{5}=11$, ..., and so on. What is the value of $a^{n}+b^{n}$ when $n=11$?<|im_end|>
<|im_start|>assistant
<Z_64><Z_78><Z_121><Z_50><Z_111><Z_108><Z_73><Z_96><Z_46><Z_125><Z_100><Z_10><ANSWER>

Question: Observe the following equations: $a+b=1$, $a^{2}+b^{2}=3$, $a^{3}+b^{3}=4$, $a^{4}+b^{4}=7$, $a^{5}+b^{5}=11$, ..., and so on. What is the value of $a^{n}+b^{n}$ when $n=11$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = \cos x + \sqrt{3}\sin x$, find the value of ${f'}(\frac{π}{3})$.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = \cos x + \sqrt{3}\sin x$, find the value of ${f'}(\frac{π}{3})$.<|im_end|>
<|im_start|>assistant
<Z_113><Z_115><Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = \cos x + \sqrt{3}\sin x$, find the value of ${f'}(\frac{π}{3})$.<|im_end|>
<|im_start|>assistant
<Z_89><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given the function $f(x) = \cos x + \sqrt{3}\sin x$, find the value of ${f'}(\frac{π}{3})$.<|im_end|>
<|im_start|>assistant
<Z_79><Z_52><Z_74><ANSWER>

Question: Given the function $f(x) = \cos x + \sqrt{3}\sin x$, find the value of ${f'}(\frac{π}{3})$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the tens digit and the ones digit of the integer form of $(3+4)^{15}$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the tens digit and the ones digit of the integer form of $(3+4)^{15}$?<|im_end|>
<|im_start|>assistant
<Z_113><Z_79><Z_91><Z_32><Z_66><Z_49><Z_20><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the tens digit and the ones digit of the integer form of $(3+4)^{15}$?<|im_end|>
<|im_start|>assistant
<Z_24><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the tens digit and the ones digit of the integer form of $(3+4)^{15}$?<|im_end|>
<|im_start|>assistant
<Z_30><Z_67><Z_115><Z_117><Z_107><Z_104><Z_11><Z_118><ANSWER>

Question: What is the sum of the tens digit and the ones digit of the integer form of $(3+4)^{15}$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An athlete runs a certain distance in 20 seconds. His speed is 36 km/h. What is the distance he ran?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An athlete runs a certain distance in 20 seconds. His speed is 36 km/h. What is the distance he ran?<|im_end|>
<|im_start|>assistant
<Z_57><Z_51><Z_108><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An athlete runs a certain distance in 20 seconds. His speed is 36 km/h. What is the distance he ran?<|im_end|>
<|im_start|>assistant
<Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
An athlete runs a certain distance in 20 seconds. His speed is 36 km/h. What is the distance he ran?<|im_end|>
<|im_start|>assistant
<Z_81><Z_84><Z_74><ANSWER>

Question: An athlete runs a certain distance in 20 seconds. His speed is 36 km/h. What is the distance he ran?


Question:
Given $DC = 9$, $CB = 10$, $AB = \frac{1}{3}AD$, and $ED = \frac{2}{3}AD$, find $FC$. Express your answer as a decimal.
[asy]
draw((0,0)--(-30,0)--(-30,24)--cycle);
draw((-19,0)--(-19,16));
draw((-10,0)--(-10,6));
draw((-10,0.5)--(-10+0.5,0.5)--(-10+0.5,0));
draw((-19,0.5)--(-19+0.5,0.5)--(-19+0.5,0));
draw((-30,0.5)--(-30+0.5,0.5)--(-30+0.5,0));
label("A",(0,0),E);
label("B",(-10,0),S);
label("G",(-10,6),N);
label("C",(-19,0),S);
label("F",(-19,16),N);
label("D",(-30,0),S);
label("E",(-30,24),N);
[/asy]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $a$ and $b$ are two non-collinear unit vectors, if the vector $a+b$ is perpendicular to the vector $ka-b$, then the real number $k=$ ▲.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $a$ and $b$ are two non-collinear unit vectors, if the vector $a+b$ is perpendicular to the vector $ka-b$, then the real number $k=$ ▲.<|im_end|>
<|im_start|>assistant
<Z_113><Z_86><Z_34><Z_39><Z_82><Z_53><Z_39><Z_5><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $a$ and $b$ are two non-collinear unit vectors, if the vector $a+b$ is perpendicular to the vector $ka-b$, then the real number $k=$ ▲.<|im_end|>
<|im_start|>assistant
<Z_20><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given that $a$ and $b$ are two non-collinear unit vectors, if the vector $a+b$ is perpendicular to the vector $ka-b$, then the real number $k=$ ▲.<|im_end|>
<|im_start|>assistant
<Z_103><Z_48><Z_57><Z_94><Z_39><Z_75><Z_0><Z_56><ANSWER>

Question: Given that $a$ and $b$ are two non-collinear unit vectors, if the vector $a+b$ is perpendicular to the vector $ka-b$, then the real number $k=$ ▲.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the difference between the largest number and the least number written with the digits 9, 3, 1, 2?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the difference between the largest number and the least number written with the digits 9, 3, 1, 2?<|im_end|>
<|im_start|>assistant
<Z_57><Z_110><Z_36><Z_49><Z_30><Z_78><Z_93><Z_99><Z_73><Z_11><Z_73><Z_93><Z_123><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the difference between the largest number and the least number written with the digits 9, 3, 1, 2?<|im_end|>
<|im_start|>assistant
<Z_127><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the difference between the largest number and the least number written with the digits 9, 3, 1, 2?<|im_end|>
<|im_start|>assistant
<Z_30><Z_104><Z_95><Z_15><Z_106><Z_21><Z_51><Z_0><Z_72><Z_54><Z_32><Z_71><Z_90><Z_19><ANSWER>

Question: What is the difference between the largest number and the least number written with the digits 9, 3, 1, 2?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of the triangle with vertices $(4, -3)$, $(-1, 2)$, and $(2, -7)$.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of the triangle with vertices $(4, -3)$, $(-1, 2)$, and $(2, -7)$.<|im_end|>
<|im_start|>assistant
<Z_104><Z_86><Z_91><Z_87><Z_66><Z_124><Z_11><Z_45><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of the triangle with vertices $(4, -3)$, $(-1, 2)$, and $(2, -7)$.<|im_end|>
<|im_start|>assistant
<Z_127><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the area of the triangle with vertices $(4, -3)$, $(-1, 2)$, and $(2, -7)$.<|im_end|>
<|im_start|>assistant
<Z_20><Z_61><Z_85><Z_21><Z_20><Z_1><Z_48><Z_46><ANSWER>

Question: Find the area of the triangle with vertices $(4, -3)$, $(-1, 2)$, and $(2, -7)$.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|im_end|>
<|im_start|>assistant
<Z_57><Z_70><Z_36><Z_62><Z_103><Z_96><Z_16><Z_76><Z_54><Z_75><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|im_end|>
<|im_start|>assistant
<Z_71><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?<|im_end|>
<|im_start|>assistant
<Z_53><Z_96><Z_66><Z_84><Z_21><Z_30><Z_35><Z_82><Z_45><Z_91><ANSWER>

Question: The prime factorization of 4410 is $2 \times 3^2 \times 5 \times 7^2$. How many of its positive integer factors are perfect squares?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|im_end|>
<|im_start|>assistant
<Z_94><Z_99><Z_82><Z_43><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|im_end|>
<|im_start|>assistant
<Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.<|im_end|>
<|im_start|>assistant
<Z_109><Z_45><Z_52><Z_85><Z_92><ANSWER>

Question: Given a sequence $\left\{a_{n}\right\}$ with 9 terms, where $a_{1}=a_{9}=1$, and for each $i \in \{1,2, \cdots, 8\}$, $\frac{a_{i+1}}{a_{i}} \in \left\{2,1,-\frac{1}{2}\right\}$, determine the number of such sequences.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|im_end|>
<|im_start|>assistant
<Z_104><Z_93><Z_50><Z_110><Z_79><Z_93><Z_107><Z_114><Z_114><Z_114><Z_80><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|im_end|>
<|im_start|>assistant
<Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?<|im_end|>
<|im_start|>assistant
<Z_45><Z_23><Z_10><Z_4><Z_13><Z_44><Z_119><Z_93><Z_67><Z_3><Z_111><ANSWER>

Question:
During a week, each day Carla counts different items in her school:

On Monday, she counts the tiles on the floor in her homeroom (60 tiles), the books in the shelves (120 books), and the windows (10 windows) twice. On Tuesday, Carla alternates the count: she counts all the tiles three times, the books twice, and the windows once. On Wednesday, she counts the chairs in the cafeteria (80 chairs) four times and the light bulbs (24 light bulbs) five times.

On Thursday, she counts items in geometric progression: she counts the tiles once, the chairs twice, the books three times, the windows four times, and finishes with counting the light bulbs five times. On Friday, she applies a Fibonacci sequence to her counting: she counts the tiles once, the books and the chairs twice each, and the windows and the light bulbs three times each.

If counting each item individually counts as one, how many times has Carla counted things in her school over the course of the entire week?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|im_end|>
<|im_start|>assistant
<Z_113><Z_108><Z_108><Z_87><Z_86><Z_115><Z_89><Z_52><Z_65><Z_99><Z_49><Z_66><Z_76><Z_76><Z_49><Z_114><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|im_end|>
<|im_start|>assistant
<Z_16><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.<|im_end|>
<|im_start|>assistant
<Z_90><Z_7><Z_34><Z_123><Z_51><Z_82><Z_53><Z_104><Z_127><Z_61><Z_118><Z_73><Z_79><Z_88><Z_64><Z_87><ANSWER>

Question: If $a$ and $b$ are positive integers, and $143a + 500b = 2001$, then the value of $a + b$ is.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_30><Z_105><Z_73><Z_107><Z_63><Z_99><Z_75><Z_70><Z_124><Z_58><Z_48><Z_55><Z_58><Z_34><Z_39><Z_56><Z_70><Z_10><Z_101><Z_126><Z_61><Z_47><Z_101><Z_49><Z_58><Z_96><Z_5><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|im_end|>
<|im_start|>assistant
<Z_60><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?<|im_end|>
<|im_start|>assistant
<Z_20><Z_106><Z_116><Z_64><Z_18><Z_88><Z_28><Z_101><Z_104><Z_12><Z_114><Z_8><Z_111><Z_113><Z_124><Z_63><Z_38><Z_26><Z_64><Z_42><Z_44><Z_118><Z_58><Z_56><Z_124><Z_15><Z_110><Z_95><Z_68><ANSWER>

Question: A four-digit integer $p$ and the four-digit integer obtained by reversing the order of the digits of $p$ are both divisible by 63. If $p$ is also divisible by 11, what is the greatest possible value of $p$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|im_end|>
<|im_start|>assistant
<Z_104><Z_66><Z_126><Z_81><Z_96><Z_39><Z_65><Z_41><Z_11><Z_72><Z_91><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|im_end|>
<|im_start|>assistant
<Z_65><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?<|im_end|>
<|im_start|>assistant
<Z_19><Z_57><Z_105><Z_70><Z_116><Z_76><Z_48><Z_5><Z_84><Z_23><Z_43><ANSWER>

Question: a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|im_end|>
<|im_start|>assistant
<Z_94><Z_59><Z_68><Z_87><Z_64><Z_40><Z_93><Z_92><Z_33><Z_66><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|im_end|>
<|im_start|>assistant
<Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.<|im_end|>
<|im_start|>assistant
<Z_108><Z_99><Z_107><Z_107><Z_107><Z_23><Z_8><Z_87><Z_89><Z_126><ANSWER>

Question: A worker is paid Rs. 25/- for a full day of work on Task A and Rs. 30/- for a full day of work on Task B. In a week, he works three days on Task A, two days on Task B, and one day on Task A with 2 hours of overtime before taking a day off. Overtime is paid at 1.5 times the regular hourly rate for the task, and he receives a performance bonus of Rs. 50/- in the same week. Additionally, the worker has Rs. 40/- deducted for a weekly transportation expense. Calculate the worker's total payment for the week, considering all variables.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|im_end|>
<|im_start|>assistant
<Z_94><Z_1><Z_97><Z_31><Z_34><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|im_end|>
<|im_start|>assistant
<Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]<|im_end|>
<|im_start|>assistant
<Z_124><Z_74><Z_34><Z_81><Z_33><ANSWER>

Question: There exist $r$ unique nonnegative integers $n_1 > n_2 > \cdots > n_r$ and $r$ unique integers $a_k$ ($1\le k\le r$) with each $a_k$ either $1$ or $-1$ such that\[a_13^{n_1} + a_23^{n_2} + \cdots + a_r3^{n_r} = 2022.\]


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|im_end|>
<|im_start|>assistant
<Z_126><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.<|im_end|>
<|im_start|>assistant
<Z_47><ANSWER>

Question: Let's modify the original problem by increasing the minimum area requirement to 150 sq. ft and making the length 20 ft longer than the width. Determine the minimum width needed for a rectangular area to meet these new constraints.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|im_end|>
<|im_start|>assistant
<Z_104><Z_105><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|im_end|>
<|im_start|>assistant
<Z_64><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?<|im_end|>
<|im_start|>assistant
<Z_49><Z_26><ANSWER>

Question: What is the sum of the squares of the coefficients of $5(x^4 + 4x^3 + 2x^2 + 1)$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|im_end|>
<|im_start|>assistant
<Z_94><Z_59><Z_34><Z_34><Z_96><Z_90><Z_75><Z_33><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|im_end|>
<|im_start|>assistant
<Z_61><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.<|im_end|>
<|im_start|>assistant
<Z_9><Z_104><Z_84><Z_57><Z_127><Z_14><Z_104><Z_28><ANSWER>

Question:
Find the maximum number of real roots to a polynomial of the form
\[ ax^n + x^{n-1} + \dots + x + 1 = 0, \]
where \( n \) is a positive even integer, and \( a \) is a real number not equal to 0.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|im_end|>
<|im_start|>assistant
<Z_57><Z_63><Z_123><Z_80><Z_93><Z_66><Z_61><Z_124><Z_96><Z_20><Z_91><Z_121><Z_22><Z_28><Z_123><Z_37><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|im_end|>
<|im_start|>assistant
<Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?<|im_end|>
<|im_start|>assistant
<Z_72><Z_32><Z_99><Z_78><Z_15><Z_20><Z_61><Z_46><Z_61><Z_33><Z_20><Z_48><Z_56><Z_3><Z_29><Z_71><ANSWER>

Question: Find the number of moles of H2O formed on combining some moles of HCl and 3 moles of NaHCO3, if the reaction produces 3 moles of H2O. How many moles of HCl are used?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?<|im_end|>
<|im_start|>assistant
<Z_77><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?<|im_end|>
<|im_start|>assistant
<Z_120><ANSWER>

Question: In how many different ways can six students stand in a straight line if three of the students, who are friends, refuse to stand next to each other?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|im_end|>
<|im_start|>assistant
<Z_94><Z_91><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|im_end|>
<|im_start|>assistant
<Z_109><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.<|im_end|>
<|im_start|>assistant
<Z_57><Z_68><Z_82><ANSWER>

Question: Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits, where the hundreds digit is 8.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|im_end|>
<|im_start|>assistant
<Z_104><Z_68><Z_93><Z_124><Z_119><Z_80><Z_72><Z_101><Z_5><Z_54><Z_63><Z_95><Z_82><Z_5><Z_98><Z_83><Z_118><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|im_end|>
<|im_start|>assistant
<Z_32><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?<|im_end|>
<|im_start|>assistant
<Z_87><Z_116><Z_56><Z_113><Z_101><Z_26><Z_53><Z_16><Z_64><Z_20><Z_62><Z_12><Z_9><Z_19><Z_124><Z_34><Z_16><ANSWER>

Question: Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|im_end|>
<|im_start|>assistant
<Z_94><Z_59><Z_115><Z_120><Z_65><Z_119><Z_93><Z_95><Z_96><Z_119><Z_125><Z_101><Z_79><Z_90><Z_63><Z_95><Z_24><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|im_end|>
<|im_start|>assistant
<Z_95><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?<|im_end|>
<|im_start|>assistant
<Z_113><Z_16><Z_59><Z_105><Z_2><Z_14><Z_24><Z_41><Z_86><Z_63><Z_71><Z_56><Z_84><Z_40><Z_115><Z_108><Z_58><Z_41><ANSWER>

Question: Safari National park has 100 lions, half as many snakes, 10 fewer giraffes than snakes, and a number of elephants equal to quarter times the number of lions. On the other hand, Savanna National park has double as many lions as Safari National park, triple as many snakes as Safari National park, and 20 more giraffes than Safari National park. Savanna National park also has 5 times as many elephants as Safari National park, and a number of zebras half of the total number of lions and snakes combined. How many animals in total does Savanna National park have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the greatest prime factor of $2^8 + 5^5$?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the greatest prime factor of $2^8 + 5^5$?<|im_end|>
<|im_start|>assistant
<Z_57><Z_77><Z_38><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the greatest prime factor of $2^8 + 5^5$?<|im_end|>
<|im_start|>assistant
<Z_93><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the greatest prime factor of $2^8 + 5^5$?<|im_end|>
<|im_start|>assistant
<Z_25><Z_20><Z_104><ANSWER>

Question: What is the greatest prime factor of $2^8 + 5^5$?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|im_end|>
<|im_start|>assistant
<Z_104><Z_73><Z_79><Z_50><Z_119><Z_80><Z_59><Z_78><Z_103><Z_78><Z_78><Z_61><Z_32><Z_79><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|im_end|>
<|im_start|>assistant
<Z_12><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?<|im_end|>
<|im_start|>assistant
<Z_123><Z_53><Z_44><Z_54><Z_127><Z_9><Z_69><Z_87><Z_19><Z_96><Z_53><Z_10><Z_76><Z_8><ANSWER>

Question: Consider two positive odd integers less than $20$ (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|im_end|>
<|im_start|>assistant
<Z_57><Z_74><Z_65><Z_96><Z_126><Z_107><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|im_end|>
<|im_start|>assistant
<Z_31><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.<|im_end|>
<|im_start|>assistant
<Z_22><Z_73><Z_13><Z_59><Z_123><Z_6><ANSWER>

Question: The third term of a geometric sequence of positive numbers is $16$ and the seventh term is $2$. What is the fifth term of the sequence? Express your answer in simplest radical form.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of \(635^2 - 615^2\)?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of \(635^2 - 615^2\)?<|im_end|>
<|im_start|>assistant
<Z_57><Z_106><Z_34><Z_77><Z_20><Z_65><Z_28><Z_66><Z_41><Z_59><Z_16><Z_75><Z_96><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of \(635^2 - 615^2\)?<|im_end|>
<|im_start|>assistant
<Z_85><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the value of \(635^2 - 615^2\)?<|im_end|>
<|im_start|>assistant
<Z_5><Z_105><Z_46><Z_82><Z_83><Z_115><Z_8><Z_66><Z_78><Z_67><Z_9><Z_17><Z_100><ANSWER>

Question: What is the value of \(635^2 - 615^2\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|im_end|>
<|im_start|>assistant
<Z_104><Z_77><Z_97><Z_78><Z_36><Z_37><Z_38><Z_49><Z_119><Z_87><Z_48><Z_70><Z_125><Z_83><Z_12><Z_119><Z_123><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|im_end|>
<|im_start|>assistant
<Z_52><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?<|im_end|>
<|im_start|>assistant
<Z_23><Z_17><Z_23><Z_81><Z_32><Z_111><Z_86><Z_2><Z_65><Z_107><Z_83><Z_108><Z_27><Z_106><Z_93><Z_60><Z_39><ANSWER>

Question: John wants to start a zoo. He has 15 snakes, twice as many monkeys as he does snakes, 5 fewer lions than he does monkeys, 8 more pandas than he does lions, and 1/3 as many dogs as he does pandas. How many total animals does John have?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|im_end|>
<|im_start|>assistant
<Z_104><Z_103><Z_115><Z_103><Z_33><Z_37><Z_124><Z_107><Z_59><Z_114><Z_87><Z_12><Z_65><Z_52><Z_52><Z_72><Z_70><Z_41><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|im_end|>
<|im_start|>assistant
<Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?<|im_end|>
<|im_start|>assistant
<Z_119><Z_58><Z_26><Z_50><Z_89><Z_52><Z_52><Z_94><Z_33><Z_104><Z_45><Z_44><Z_39><Z_89><Z_74><Z_87><Z_30><Z_105><ANSWER>

Question: The company's data entry team had 5 employees working on a large project. Rudy types 64 words per minute, Joyce types 76 words per minute, Gladys types 91 words per minute, Lisa types 80 words per minute and Mike types 89 words per minute. What is the team's average typed words per minute?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|im_end|>
<|im_start|>assistant
<Z_104><Z_115><Z_43><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|im_end|>
<|im_start|>assistant
<Z_36><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.<|im_end|>
<|im_start|>assistant
<Z_16><Z_110><Z_13><ANSWER>

Question: In an opaque bag, there are several red and white balls, which are identical except for their colors. There are $12$ red balls in the bag, and the probability of drawing a white ball from the bag is $\frac{2}{3}$. Find the number of white balls in the bag.


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?<|im_end|>
<|im_start|>assistant
<Z_57><Z_12><Z_65><Z_62><Z_81><Z_47><Z_91><Z_59><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?<|im_end|>
<|im_start|>assistant
<Z_51><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?<|im_end|>
<|im_start|>assistant
<Z_110><Z_19><Z_33><Z_85><Z_121><Z_55><Z_76><Z_54><ANSWER>

Question: A dog is tied to a tree by a long nylon cord of a certain length. The dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all times. The dog ran approximately 30 feet. What was the approximate length of the nylon cord?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|im_end|>
<|im_start|>assistant
<Z_94><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|im_end|>
<|im_start|>assistant
<Z_57><Z_93><Z_1><Z_121><Z_103><Z_81><Z_72><Z_124><Z_95><Z_78><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|im_end|>
<|im_start|>assistant
<Z_0><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?<|im_end|>
<|im_start|>assistant
<Z_87><Z_27><Z_50><Z_9><Z_125><Z_89><Z_8><Z_10><Z_60><Z_56><ANSWER>

Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. If his savings at the end of a month are Rs. 1500, what is his monthly salary?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|im_end|>
<|im_start|>assistant
<Z_57><Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|im_end|>
<|im_start|>assistant
<Z_113><Z_77><Z_43><Z_49><Z_82><Z_82><Z_71><Z_73><Z_32><Z_95><Z_45><Z_71><Z_47><Z_26><Z_92><Z_39><Z_63><Z_124><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|im_end|>
<|im_start|>assistant
<Z_85><Z_102><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?<|im_end|>
<|im_start|>assistant
<Z_52><Z_62><Z_74><Z_52><Z_19><Z_9><Z_25><Z_1><Z_26><Z_39><Z_48><Z_72><Z_69><Z_84><Z_124><Z_24><Z_45><Z_120><ANSWER>

Question: What is the least number that should be added to 1100, so the sum of the number is completely divisible by 37? Additionally, what is the least number to be subtracted from 1100 to make it completely divisible by 37?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|im_end|>
<|im_start|>assistant
<Z_57><Z_27><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|im_end|>
<|im_start|>assistant
<Z_94><Z_100><Z_99><Z_119><Z_65><Z_126><Z_79><Z_28><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|im_end|>
<|im_start|>assistant
<Z_29><Z_125><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?<|im_end|>
<|im_start|>assistant
<Z_48><Z_72><Z_117><Z_100><Z_113><Z_127><Z_118><Z_46><ANSWER>

Question:
A certain supermarket offers discounts on two types of products, A and B. Product A is discounted by 20%, and product B is discounted by 25%. It is known that before the discount, buying 6 units of product A and 3 units of product B costs $600. After the discount, buying 50 units of product A and 40 units of product B costs $5200.
$(1)$ What is the price of each unit of product A and product B before the discount?
$(2)$ If a person buys 80 units of product A and 100 units of product B, how much money can be saved by buying these products after the discount compared to not having any discount?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|im_end|>
<|im_start|>assistant
<Z_94><Z_110><Z_119><Z_114><Z_103><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|im_end|>
<|im_start|>assistant
<Z_0><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?<|im_end|>
<|im_start|>assistant
<Z_23><Z_89><Z_120><Z_112><Z_51><ANSWER>

Question: If \(x\), \(y\), and \(z\) are distinct positive integers such that \(x^2 + y^2 = z^3\), what is the smallest possible value of \(x + y + z\)?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|im_end|>
<|im_start|>assistant
<Z_57><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|im_end|>
<|im_start|>assistant
<Z_113><Z_13><Z_1><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|im_end|>
<|im_start|>assistant
<Z_118><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?<|im_end|>
<|im_start|>assistant
<Z_103><Z_39><Z_52><ANSWER>

Question: A cube with a certain edge length is cut into 1 cm cubes, resulting in a 600% increase in the surface area. What is the edge length of the original cube?


<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|im_end|>
<|im_start|>assistant
<Z_104><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|im_end|>
<|im_start|>assistant
<Z_104><Z_103><Z_12><Z_121><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|im_end|>
<|im_start|>assistant
<Z_89><ANSWER>

<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.<|im_end|>
<|im_start|>assistant
<Z_90><Z_37><Z_35><Z_46><ANSWER>

Question: Among all numbers of the form \(36^m - 5^n\), where \(m\) and \(n\) are natural numbers, find the one with the smallest absolute value.