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Palindromic DNA Description: A DNA sequence is composed of a series of four possible nucleobases, namely Adenine, Guanine, Thymine and Cytosine; we will refer to each of these bases by their initial. For our purposes, nucleobases have an associated cyclic “order”: A is followed by G, which in turn is f...
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Palindromic Naming Description: Yraglac is expecting to have a child in the near future. Being a mathematically-minded person, he would like his child’s name to be a palindrome – that is, reads the same when read forward and backward. Given a name, he would like to count the number of ways he can creat...
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Palindromic Password Description: The IT department at your school decided to change their password policy. Each password will have to consist of $N$ $6$-digit numbers separated by dashes, where $N$ will be determined by the phase of the moon and the weather forecast for the day after it will be ge...
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Palindromic Word Search Description: Given a rectangular grid of uppercase letters, find a rectangular region of the grid of maximum possible area such that there is a horizontal palindrome spanning some row of the rectangular region and a vertical palindrome spanning some column of the rectangular reg...
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Pallatölur Description: Palli loves prime numbers but his favourite numbers are even prime numbers. Palli received numbers from his grandmother as a birthday present, but he only wants to hold on to his favourite numbers. The set of numbers his grandmother bought included all the integers from $a$ to ...
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Paludarium Description: Feeling lonely in his apartment since he is quarantined inside at the moment, Bob decided to make use of the fish tank left by the previous renter to set up a little paludarium (a semi-aquatic habitat that combines land and water environments) and fill it with little creatures t...
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Panda Chess Description: In the city of Pandaville, the predominant black and white colours of the inhabitants have somehow made chess a very popular game in the area. There are a total of $N$ chess players in the city and they are very competitive. Recently, the annual Panda Chess Tournament has just ...
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Panda Preserve Description: Last month, Sichuan province secured funding to establish the Great Panda National Park, a natural preserve for a population of more than $1\, 800$ giant pandas. The park will be surrounded by a polygonal fence. In order for researchers to track the pandas, wireless rece...
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Pandemic Shopping Description: In response to the COVID-19 pandemic, most retail stores instituted a variety of restrictions on customer behaviour in order to comply with government social/physical distancing rules. In particular, many stores placed arrow markers on aisle floors to direct the flow of c...
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Paper Snowflakes Description: To make a paper snowflake, you fold a sheet of paper in various places and then cut some parts out of the folded sheet. When you unfold the sheet, it can make a very nice pattern. That is, if the folds and cuts are chosen well. Samantha has recently taken up this hobby but wi...
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Parades Description: In The City of Eternal Festivities, there are $n$ street junctions and $n - 1$ bidirectional streets, each street connecting two of the junctions. Between every two junctions, there is exactly one (direct or indirect) path connecting them. No junction is an endpoint for more than $...
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Paradox With Averages Description: Note that this is an easier version of the problem averageshard. One well-known joke goes as follows: If a bad Computer Science student drops out of college and goes to a different college to study Economics instead, he will increase the average intelligence on both ...
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Paradox With Averages (Hard) Description: Note that this is a harder version of the problem averageseasy. One well-known joke goes as follows: If a bad Computer Science student drops out of college and goes to a different college to study Economics instead, he will increase the average intelligence on...
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Parakoopa Projectile Description: There are $N$ Parakoopas scattered across the first quadrant of the Cartesian plane (positive $x$ and $y$ coordinates), and Mario stands at the origin, located at $(0,0)$, waiting to put a well-known proverb to the test. He wants to hit two parakoopas (he’s fine ...
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Parallel Analysis Description: Today’s computer architectures are moving away from single processing cores toward multiple cores. Due to this shift, many computer programmers are honing their parallel programming skills to take advantage of new hardware capabilities. Writing efficient parallel programs ca...
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Parent Gap Description: In North America, and in many countries around the world, Mother’s Day is celebrated on the second Sunday in May, and Father’s Day is celebrated on the third Sunday in June. The interval between Mother’s Day and Father’s Day in any particular year, sometimes referred to as the p...
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Parket Description: Ivica has set up a new parquet flooring in his room. The room is $L$ decimeters long and $W$ decimeters wide. The blocks are of quadratic shape and each has an area of one quadratic decimeter. Once Ivica had set up the flooring, which consists of brown-colored blocks, he decide...
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Parking Description: Long Street is a straight line, where all positions are integer. You pay for parking in a specific slot, which is an integer position on Long Street. Michael does not want to pay for more than one parking though. He is very strong, and does not mind carrying all the bags around. #...
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Parking Description: Having dropped out of school because of chemistry, Luka got a job driving trucks. One evening he parked his three trucks in a rest area which charges for parking in an unusual way – they give a discount on quantity. When only one truck is parked, the driver pays $A$ kuna per minute. W...
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Parking Lot Description: Imagine you are walking across a parking lot of $r$ rows and $c$ columns of parking spots. All parking spots have a size of a unit square. A parking spot either is empty or contains a parked car. You can walk across an empty parking spot in any direction, but can only walk along ...
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Parovi Description: The distance between two integers is defined as the sum of the absolute result of subtracting their digits. For example, the distance between the numbers 4561 and 3278 is $|4 - 3| + |5 - 2| + |6 - 7| + |1 - 8| = 12$. If one of the numbers consists of fewer digits than the other,...
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Parovi Description: Mirko and Slavko are playing a game. Mirko’s turn is first and he chooses a non-empty set of pairs of numbers between $1$ and $N$ (inclusive) under the condition that the numbers that comprise a pair are mutually relatively prime. The numbers that comprise a pair must be different. ...
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Parsing Hex Description: This problem is simple. Just search the input for hexadecimal numbers, and print any numbers you find in both hexadecimal and decimal format. ## Input Input is a sequence of at most $100$ text lines, ending at end of file. Each line has at most 100 characters, and may contain one...
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Partial Linear Equation Solver Description: ## Input There are several test cases. Each test case begins with a line containing an integer $n$, where $1 \leq n \leq 100$. Then follow $n$ lines, each containing $n$ floating point numbers. The $j$:th number on the $i$:th row gives the entry $a_{i,j}$ o...
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Particle Collision Description: Particle colliders are difficult to build and experiments are costly to run. Before running any real experiments it is better to do a simulation to test out the ideas first. You are required to write a very simple simulator for this problem. There are only three particles i...
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Particle Swapping Description: The research team of prof. Feynmansson is preparing a new groundbreaking experiment in particle physics. On a special plate they have prepared a system consisting of a number of nodes connected via wires1. In the beginning of the experiment a pair of particles appears at ...
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Party Game Description: Lord Kevin (purportedly a distant relative of Lord Kelvin) is holding a party to celebrate his recent entrance into the British nobility. The exact process whereby Kevin acquired his title is a matter of some dispute, and there are even whispered rumours of identity theft, but f...
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Pascal Description: Little Frane is already in tenth grade, but is still struggling with Pascal in computer class. For homework, his teacher wrote the following program into his notebook, and he needs to determine the output, given the integer $N$. ``` readln(N); counter := 0; for i := N - 1 downto 1 do b...
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Pascal Meets Boole Description: Many people are familiar with Pascal’s Triangle, a triangular arrangement of integers named after the French mathematician and philosopher Blaise Pascal (1623–1662). If we number the rows of Pascal’s Triangle $1, 2, 3, \ldots ,$ starting from the top, then row $r$ contai...
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Pascal Multiple Description: The $(i,j)$th binomial coefficient, denoted $C(i,j)$, is the (zero-indexed) $j$th entry of the (zero-indexed) $i$th row in Pascal’s triangle: ``` 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 ... ``` where $C(0,0) = 1$ and the $(i+1)$st row can be computed from the $i$th row ...
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Pascal's Hyper-Pyramids Description: We programmers know and love Pascal’s triangle: an array of numbers with $1$ at the top and whose entries are the sum of the two numbers directly above (except numbers at both ends, which are always $1$). For programming this generation rule, the triangle is bes...
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Pasijans Description: Pasijans, patience, or solitaire is the name for a group of single player card games. One new such game, so new it has no name, is played with cards sporting random integers as values. The game starts by shuffling all cards and distributing them in $N$ sequences, not necessari...
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Passing Secrets Description: In the public school system, passing secret messages between students is a serious enterprise with a proud, noble history. At the Junior Computer Scientist High School, industrious students have discovered the idea of peer-to-peer networking and have adapted this to message...
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Passport Stamps Description: You just got your new passport, fresh with pages ready to be stamped by immigration officers. Sadly, because your passport has so many pages, immigration officers are too lazy to try to use your pages efficiently, so you may need to get a new passport sooner than you think....
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Password Hacking Description: You have done a lot of hacking using such lists, and you have a good idea of how likely each password in the list is the correct one (you are very surprised by the number of people using “123456” as their passwords). You have a new account to hack, and you have decided to ...
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Password Rotation Description: Yraglac recently found a list of compromised passwords for a major online website and would like to analyze the data to find out if any two users have similar passwords. Two passwords are considered similar if they are rotations or reverse rotations of each other. The rot...
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Passwords Description: It’s that time of the year again when you go back to work and need to choose new passwords for all your services. The rules enforced by the system administrators are very strict, and the password you choose must obey the following restrictions: * It must contain only letters and...
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Patchwork Description: Adam’s grandmother has a birthday coming up and he wants to make her a beautiful patchwork quilt as a present. He has created a collection of patch designs that he will sew onto the quilt. However, he is having trouble deciding exactly where to place his patches. His current proc...
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Path Crossings Description: Yraglac is the developer of a popular Android/iOS racing game that also happens to collect location data from its players all the time, even when the player is not using the app. He has now amassed a large database of the precise location $(x,y)$ of players over time $(t...
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Path Tracing Description: Billy likes to wander around. Each day he follows a sequence of up, down, left and right moves. At the end of the day, he would like to know where he’s been. You are going to help by providing Billy with a program that draws a map for him. The program should read a sequence of...
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Paths Description: A graph is a mathematical structure which consists of a set of vertices, and a set of edges, each connecting two vertices. An example of a graph with $4$ vertices and $3$ edges is shown in the sample explanation below. A path in the graph is defined as an ordered list of $2$...
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Patrick's Triangle Description: Patrick is an unknown mathematician that wanted to become famous. Patrick had heard that the mathematician Blaise Pascal had became famous because of his triangle, Pascal’s triangle. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 Patrick thought that if he could come up with ...
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Patuljci Description: Every day, while the dwarves are busy in the mines, Snow White prepares dinner for them; seven chairs, seven plates, seven forks and seven knives for seven hungry dwarves. One day nine dwarves came from the mines instead of seven (nobody knows how or why), each of them claiming to be...
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Patuljci Description: Snow White and the $N$ dwarfs live in the forest. While the dwarfs mine away Snow White hangs around social networks. Each morning the dwarfs form a long line and go whistling away to the mine. Snow White runs around them and snaps pictures to upload onto her favorite social netw...
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Paul Eigon Description: Paul Eigon recently got a new job at a famous company in town. They have all sorts of cool stuff at the office. Video games, a swimming pool, a sauna, and even a ping-pong table! Paul really loves his enjoyable new workplace. Mr. Eigon plays a lot of ping-pong at work. While he is ...
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Pavers Description: In the land of Quendor, walkways, sidewalks and hallways are always $2$ mb (mini-bloit, roughly $\frac{1}{2000}$ of a bloit) in width. J. Pierpont Flathead (pictured to the right) has hired the Frobozz Magic Paver Company to install new walkways in and around all his banks using pav...
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Pawn Shop Description: You run a tight ship at the pawn shop. You arrange certain items in the window to be displayed to the street. You sometimes display the same type of item multiple times. For simplicity, we think of the items on display as a sequence of values where the value represents the type o...
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Pea Pattern Description: Do you see the pattern in the following sequence of numbers? Each term describes the makeup of the previous term in the list. For example, the term $3112$ indicates that the previous term consisted of three $1$’s (that’s the $31$ in $3112$) and one $2$ (that’s the $12$ in $3112$)....
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Pea Soup and Pancakes Description: ## Input The first line of input contains a number $n$ ($1 \le n \le 10$), the number of restaurants. Then follow the $n$ restaurant menus. Each menu starts with a line containing a number $k$ ($1 \le k \le 10$), the number of menu items for the day. The remainde...
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Peach Powder Polygon Description: After rescuing Prince Mario, Peach finds herself trapped in a polygonal world consisting of many castles. She knows that even though she defeated Bowser, Bowser’s unknown cousin Powder is coming after her. Peach runs from castle $1$ to castle $2$ as fast as she can, and as...
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Peak Tower Description: After taking the Peak Tram, you reach the Peak Tower — an ideal place to take a picture of the Victoria Harbour. Being a must-see attraction, the Peak Tower is packed with tourists, and it’s pretty hard to take a picture without many people blocking the beautiful scene. Occasio...
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Peak Tram Description: Inspired by the Peak Tram in Hong Kong, you are going to build your own peak tram on a hill, together with the buildings near it. The peak tram and the buildings are aligned on a straight line. The peak tram is at position $0$ on the line. There are $n$ buildings, where build...
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Pear-wise Voting Description: Bob Roberts is ending his term as president of a local group of fruit aficionados call the Pear-wise Club. Being president is a plum position so many people are running, some of whom Bob thinks are just peachy, while others are just the pits. After some thought, Bob has am...
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Pearls Description: Nikoli’s Jewelry Store in Puzzletown sells a line of necklaces consisting of black and white pearls. The pearls in the necklace are firmly glued to a cord of length $k$, where each unit of cord length either holds a pearl or is empty. Each necklace is displayed on a rectangular velv...
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Pearls Description: Laura likes to create pretty necklaces with pearls. She has two neckalces $A$ and $B$, which she would like to use as templates to create a new necklace. A necklace is represented by a string, where each character represents the color of a bead on the necklace. Laura furthermor...
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Pebble Solitaire Description: I bet you have seen a pebble solitaire game. You know the game where you are given a board with an arrangment of small cavities, initially all but one occupied by a pebble each. The aim of the game is to remove as many pebbles as possible from the board. Pebbles disappear ...
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Pebble Solitaire Description: I bet you have seen a pebble solitaire game. You know the game where you are given a board with an arrangment of small cavities, initially all but one occupied by a pebble each. The aim of the game is to remove as many pebbles as possible from the board. Pebbles disappear ...
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Peculiar primes Description: The level of corruption in some countries is really high. It is hard to imagine that these unethical manners have already hit the academic field. Some rumors are spreading that some students tried to bribe their lecturers to get better grades. Would you believe it? But the...
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Pedal Power Description: You’re ready to start your semester off right! Well, almost … you have everything listed on your calendar, you just bought a brand new bike, but you haven’t yet planned your commute! You are quite busy this semester, and so you decide to plan a route for all your classes and ap...
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Peer Streaming Description: It is now time to develop the logic to decide which users should send which data to which other users. At a high level, the logic works as follows. Each second, the data available at the different users listening to a song is examined. Based on this, the system decides what ...
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Peg Description: In the famous logic game Peg, pieces jump over other pieces to remove them from the game, until only one piece is left. Here is the initial layout of the board: ``` ooo ooo ooooooo ooo.ooo ooooooo ooo ooo ``` The lowercase letter ’o’ represents a piece, while the character ’.’ i...
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Peg Game for Two Description: Jacquez and Alia’s parents take them on many road trips. To keep themselves occupied, they play a triangular peg game, meant for one player. In the original game, one player has an equilateral triangle containing $15$ holes (five holes per side of the triangle). Initially ...
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Peg Solitaire Description: The game of peg solitaire, popular at the court of the French king Louis XIV, has the following rules. Given a two-dimensional board with a mesh of holes, each hole can contain one peg (pin). The only legal move of a peg is a vertical or horizontal jump over an adjacent peg i...
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Pegs Description: Little Zorro and Worro are playing an interesting game on an $n\times n$ square grid. Each game is really short: each player makes just one move. The game is played with very very thin pegs. The pegs come in two colors: black and white. Zorro goes first: he puts the pegs at the ve...
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Pegs and Legs Description: Pegs and Legs is a game where a disk slides down a nearly-vertical board. At the bottom of the board are places for the disk to land, called legs. Each leg is worth a certain amount of points if your disk lands in it. You start with a disk at the top and drop it onto some ...
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Pencil Crayons Description: Mr. Daniels bought a set of $N$ identical boxes of pencil crayons for his classroom, each containing the same set of $K$ distinct colours of pencils. Over the course of the year, the pencil crayons got mixed up between the boxes. Surprisingly, none of them have been lost (yet). ...
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Peningar Description: Tómas has found himself in a strange world. This world consists of $n$ cells arranged in a circle. Thus cells $i$ and $i+1$ are adjacent for $1 \leq i < n$, and cells $1$ and $N$ are also adjacent. In each cell there is an $a_ i$ amount of money. Tómas starts at cell $1$. In e...
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Peragrams Description: Per recently learned about palindromes. Now he wants to tell us about it and also has more awesome scientific news to share with us. “A palindrome is a word that is the same no matter whether you read it backward or forward”, Per recently said in an interview. He continued: “For...
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Perfect Date Description: Hori-san and Miyamura-kun are high-school lovers with a special kind of chemistry any modern day couple would dream for. Their ability to understand each other on a deeper level better than anyone else is something only they can understand. Just like any blossoming youthful co...
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Perfect Path Patrol Description: Citizens have formed a community watch program to ensure the streets are safe to walk at night. So, some citizens patrol certain regions of the neighborhood. These patrols are also simple: a single citizen simply patrols all streets lying on the unique path between two ...
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Perfect Porridge Description: As a true student Lucky Luke eats a big bowl of perfect porridge each morning. Luke’s goal in life is to get every chalmerist to love porridge. In the faculty there are $N$ yet-to-be-enlightened students. Luke is unfortunately not necessarily able to serve perfect porridg...
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Perfect Pth Powers Description: We say that $x$ is a perfect square if, for some integer $b$, $x = b^{2}$. Similarly, $x$ is a perfect cube if, for some integer $b$, $x = b^{3}$. More generally, $x$ is a perfect $p$th power if, for some integer $b$, $x = b^{p}$. Given an integer $x$ you are...
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Perfect Skyline Description: Zara, an aspiring architect and urban planner, has drawn out what she considers to be the perfect skyline. As Zara is still aspiring she must use her young daughter, Pippa, to test out her designs. In order to test out the designs Pippa must build them out of her building b...
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Perfect Squares Description: A famous theorem in number theory states that every positive integer can be written as the sum of four perfect squares. You have noticed, though, that usually fewer squares are enough. For example, $27$ only requires three perfect squares: $27 = 5^2 + 1^2 + 1^2$. You share...
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Perfect k-ary Tree Description: A graph $G$ is given, which is a tree with $N$ nodes. The nodes are labelled $1, 2, \dots , N$. Count the number of subgraphs of $G$ which is a perfect $k$-ary tree. An unrooted tree is called a perfect $k$-ary tree if it is possible to root the tree such tha...
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Performance Review Description: Employee performance reviews are a necessary evil in any company. In a performance review, employees give written feedback about each other on the work done recently. This feedback is passed up to their managers which then decide promotions based on the feedback received...
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Perica Description: —“I’m stopping by Žnidaršić’s house, you play the piano, Perica.” —“Ok, dad, I will!” And so, Perica began playing the piano. His piano consists of $N$ keys. Each key has a value written on it, $a_ i$. When Perica plays the piano, he presses exactly $K$ different keys at th...
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Periodic Points Description: Computing the number of fixed points and, more generally, the number of periodic orbits within a dynamical system is a question attracting interest from different fields of research. However, dynamics may turn out to be very complicated to describe, even in seemingly simple...
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Periodic Strings Description: Define a $k$-periodic string as follows: A string $s$ is $k$-periodic if the length of the string $|s|$ is a multiple of $k$, and if you chop the string up into $|s|/k$ substrings of length $k$, then each of those substrings (except the first) is the same as ...
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Periodni Description: Luka is bored in chemistry class so he is staring at a large periodic table of chemical elements hanging from a wall above the blackboard. To kill time, Luka decided to make his own table completely different from the one in the classroom. His table consists of $N$ columns, each with...
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Perket Description: "Perket" is a widely known and delicious meal. For perket to be what it is, cooks must carefully choose the ingredients to get the fullest taste possible while keeping the meal traditional. You have $N$ ingredients at your disposal. For each we know its sourness $S$ and bittern...
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PermRLE Description: You’ve invented a slight modification of the run-length encoding (RLE) compression algorithm, called PermRLE. To compress a string, this algorithm chooses some permutation of integers between 1 and $k$, applies this permutation to the first $k$ letters of the given string, then to...
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Permutation Arrays Description: Lord Pooty loves permutations. However, what’s more interesting than permutations are arrays of permutations. He has $X$, a hidden array of $m$ permutations, each of length $n$. He also has $k$ constraints regarding $X$ that will be elaborated below. A permu...
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Permutation CFG Description: Consider a permutation of the integers $1$ to $n$. Now, consider each number $1$ through $n$ to be a non-terminal in a Context-Free Grammar (CFG). Each number $k$ expands a list of the integers from $1$ to $k$ in the order of the permutation. For example, if $n=4$ and t...
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Permutation Code Description: As the owner of a computer forensics company, you have just been given the following note by a new client: I, Albert Charles Montgomery, have just discovered the most amazing cypher for encrypting messages. Let me tell you about it. To begin, you will need to decide on a...
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Permutation Descent Counts Description: Given a positive integer, $N$, a permutation of order $N$ is a one-to-one (and thus onto) function from the set of integers from $1$ to $N$ to itself. If $p$ is such a function, we represent the function by a list of its values: For example, $[5 \, 6 \, 2 \, 4 \...
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Permutation Encryption Description: Working for the Texas Spy Agency, you are in charge of writing software for handling secure communications between your clients who wish to pass you messages without anyone else being able to read them. Therefore, you have been commissioned to write a program which t...
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Permuted Arithmetic Sequence Description: An arithmetic sequence is a list of values where the difference between consecutive values is always the same. For example, $3, 7, 11, 15$ qualifies and so does $25, 15, 5, -5, -15$. However $2, 4, 7$ and $3, 6, 9, 6$ are not arithmetic sequences. ## I...
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Persistent Numbers Description: The multiplicative persistence of a number is defined by Neil Sloane (Neil J.A. Sloane in The Persistence of a Number published in Journal of Recreational Mathematics 6, 1973, pp. 97-98., 1973) as the number of steps to reach a one-digit number when repeatedly multiplyin...
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Pervasive Heart Monitor Description: You have been hired by a fitness center. You are helping to develop a system to monitor customer heart rate during exercise. While the customer stays in the gym, their heart rate is recorded at 10-minute intervals. When they leave, they can get a report of their ave...
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Pesky Heroes Description: “But, milord, then surely they will be doomed when the traps have been re-activated,” were the last words of a servant, uttered milliseconds before he…well, you get the picture. “Not necessarily, I may have to teleport my trained orcs to seal their fate. You there, figure out ...
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Pesky Mosquitoes Description: Mosquitoes are relentless this time of year! They have absolutely ruined your attempt at a picnic and it is time to take your revenge. Unfortunately, you are not well equipped to ward off these pests. All you have got at your disposal is an empty bowl that previously held ...
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Pet Description: In the popular show “Dinner for Five”, five contestants compete in preparing culinary delights. Every evening one of them makes dinner and each of other four then grades it on a scale from 1 to 5. The number of points a contestant gets is equal to the sum of grades they got. The winner...
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Pharmacy Description: Many pharmacies in the United States fill prescriptions strictly on a first-come, first-served basis, even preferring prescriptions submitted electronically from a remote site to prescriptions dropped off by waiting customers in the store. This frequently leads to situations where...
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Phone List Description: Given a list of phone numbers, determine if it is consistent in the sense that no number is the prefix of another. Let’s say the phone catalogue listed these numbers: * Emergency 911 * Alice 97 625 999 * Bob 91 12 54 26 Emergency 911 Alice 97 625 999 Bob 91 12 54 26 In this case,...
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Physical Music Description: The music business is changing rapidly, and this is reflected by the single charts. Initially, the Dutch Single Top 100 was based purely on sale numbers of CD singles. In the course of time, however, these numbers dropped dramatically, in favour of legal and illegal download...
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Physiognomy Description: A properly designed room is, as we all know, well-lit. In keeping with the teachings of Feng Shui, you have placed a number of lamps around a newly-designed room at strategic places to give it a friendlier air. Some of the lights project positive energy, and the rest give out onl...
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Pianino Description: Young Mirka is an amateur musician. She plays the multi-piano. $A$ multi-piano consists of an infinite number of multi-keys, denoted with integers that can be interpreted as the pitch. $A$ multi-composition (a composition written for a multi-piano) can be represented with a...
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Pianissimo Description: Composers use dynamics in sheet music to indicate how loud or soft the notes shall be played. Consider an $8$-scale dynamic system: * ppp: pianississimo (the softest) * pp: pianissimo (very soft) * p: piano (soft) * mp: mezzopiano (moderately soft) * mf: mezzoforte (moderately loud) *...
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Piano Lessons Description: Given Mrs. Mackenzie’s time slots, and a list of the time slots that work for each potential student, can you help her determine the maximum number of students she can fit into her schedule? Note that Mrs. Mackenzie only teaches private lessons (one student at a time) and no ...
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