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Food Carts Description: Peter is in charge of food service on a passenger train. The train has $n$ cars ordered sequentially starting from the locomotive. The $i$-th car has $p_ i$ passengers. There are $m$ food carts Peter may put into service. Each food cart serves a unique type of food. The $j$-...
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Food Mixing Description: The Volbonans of the Luncheon Kingdom are cooking their famous Stupendous Stew! For the Volbonans, Stupendous Stew is simply any soup that has saltiness level $x$ and sweetness level $y$. However, Bowser has stolen all of their ingredients! All they have left are existing soups: $...
27,701
Food Processor Description: You have a food processor with a variety of blades that can be attached to it, as well as some food you would like to process into smaller pieces. The food processor can have one blade attached at any time. Each blade processes food by reducing its average piece size at a p...
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Food Review Description: Frida is a writer for Cosmopolitan who writes restaurant reviews. She enjoys it a lot, but it seems that, throughout the years, she has reviewed all the restaurants on Earth. It’s now time to move one level up; she is going to review the food served by the airlines, so that the...
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Food Review (Hard) Description: Note that this is a bit harder version of the problem foodreview. Frida is a writer for Cosmopolitan who writes restaurant reviews. She enjoys it a lot, but it seems that, throughout the years, she has reviewed all the restaurants on Earth. It’s now time to move one lev...
27,704
Fooling Around Description: Alice and Bob take turns playing a game, with Alice going first. They begin with a pile of $N$ stones, each turn removing one less than a prime number of stones. The person who removes the last stone wins. Given $N$, determine who wins the the game, assuming Alice and Bob bo...
27,705
Foosball Dynasty Description: Balaji and his coworkers like to play Foosball on their lunch break. Foosball is a game typically played by $2$ players (individual matchup) or $4$ players (team play). However, due to the increasing interest and availability of coworkers, Balaji has created a new vari...
27,706
Football! Description: It is once again the coming of age festival for our $n$ boys in our great Kingdom. As tradition dictates, there will be a series of football games held over a span of $m$ days. Each day, there will be a football game pitting $2$ teams of $n/2$ boys against each other. Th...
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Forced Choice Description: Puff the Magic Dinosaur is a renowned magician. Due to the pandemic, he can only perform for his princess using the latest video conferencing tools. As a result, many of his usual in-person routines cannot be performed, and he must come up with a new trick. Puff has decided ...
27,708
Foreign Football Description: You are on vacation in a foreign country. This country has a local football league, and you don’t know any of the team names. However, you have found a table of all the results from this season, and next to every match is the concatenated names of the two teams that played...
27,709
Forest Construction Description: Anton, a young mathematician, comes from the cold region that is northern Sweden. He likes it there, since there are a lot of trees. Lately, however, this has made him a bit sad, since he can’t see the forest because of all the trees. Therefore, he has asked you to cons...
27,710
Forest Evolution Description: Ewan is a park ranger, and part of his duty is to observe how the ecosystem changes over time. He has just detected that a group of pine trees and aspens have started to share the same space. Before, there was a clear line between the species. This isn’t unusual, but Ewan is ...
27,711
Forest Fire Description: A fire has broken out in the integer forest! The integer forest consists of an infite two-dimensional plane where there is a tree at each point with integer coordinates. Currently, $N$ of these trees are on fire. Each minute, the fire spreads from every burning tree to its ...
27,712
Forest Fires Description: Fires can spread in a forest more easily if the trees in the forest are densely packed – it makes it easy for the fire to jump from tree to tree. Write a forest fire simulator which ‘grows’ a forest tree-by-tree. As the forest grows, your simulator should answer queries about ...
27,713
Forest Fruits Description: You stay in a cottage at a clearing in a forest. The forest consists of $V$ clearings and $E$ trails. Clearings are open spots where fruits may be found, and are numbered from $1$ to $V$. Your cottage is at clearing $1$. Trails connects two clearings. You ensure self ...
27,714
Forest Highway Description: ## Task You are given a description of the forest and the highway. The forest is a simple polygon, i.e. its sides do not cross, and the highway can be considered a straight line of width zero. You are also given $d$, the safe distance from the highway. Calculate the size of...
27,715
Forest for the Trees Description: You are playing hide-and-go-seek in a forest with Belle. The forest has one tree at each of the positive integer lattice points. That is, there is a tree at every point $(x,y)$ where $x$ and $y$ are both positive integers. You may consider each tree as a point. A logging c...
27,716
Forest for the Trees Description: You have sent a robot out into the forest, and it has gotten lost. It has a sensor that will detect all the trees around itself regardless of any occlusions, but unfortunately in this forest, all trees look alike. You do have a map of all trees in the forest, represent...
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Forest of Celery Description: Celery — the legendary Pokenom has been spotted in Alexa Forest. To become the best Pokenom trainer, Bash has arrived at Alexa Forest to capture Celery. After lots of information gathering, Bash was able to draw a map of Alexa Forest, and noted down $K$ sightings of C...
27,718
Forests Description: If a tree falls in the forest, and there’s nobody there to hear, does it make a sound? This classic conundrum was coined by George Berkeley (1685-1753), the Bishop and influential Irish philosopher whose primary philosophical achievement is the advancement of what has come to be ca...
27,719
Forever Young Description: My birthday is coming up. Alas, I am getting old and would like to feel young again. Fortunately, I have come up with an excellent way of feeling younger: if I write my age as a number in an appropriately chosen base $b$, then it appears to be smaller. For instance, suppose m...
27,720
Forgotten Homework Description: Yesterday was a fun first day of University for Alice. She met so many new people, and there were so many activities to do! But her new teacher was super strict. It was her first day of university, and the teacher still gave them a lecture on linear algebra and matrix mu...
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Formúlublað Description: ## Input The first line of the input contains two integers $1 \leq n \leq 1000$, the number of available formulas, and $1 \leq L \leq 1000$, how many lines fit on the sheet. Then there are $n$ lines, one for each formula, each containing two integers $1 \leq l_i \leq L$ an...
27,722
Fortune From Folly Description: Your friend Ómar’s favourite video game is Striker-Count. But he has now grown tired of actually playing the game and is more interested in the lootboxes found in the game. Inside each lootbox there is an item of some level of rarity. Ómar is only interested in acquiring...
27,723
Fortune Telling Description: What you see is only a moment $\dots $ In an attempt to earn enough money to support her activities, the Great Witch of Calamity has taken up a new side job: fortune telling! Her setup involves two decks of cards colored blue and black, respectively. The blue cards are num...
27,724
Fountain Description: Consider a grid consisting of $N$ rows and $M$ columns, where each cell is either air, stone, or water. Each second, the water spreads in the following fashion: * If a water cell is directly above an air cell then the air cell turns into water in the next second. * If a water ce...
27,725
Four Die Rolls Description: Ashley and Brandon are playing a game where they roll a six-sided dice four times. Each integer from $1$ to $6$ is on one face of the dice and all values are equally likely to appear. Each time they roll the dice, they write down the value that shows on the top face of the d...
27,726
Four Questions Description: It looks like taking the singles line has paid off: you’re stuck on the ski lift with a mathematician. He’s promised to show you his secret powder stash1 if you’re able to win a game against him. The game is as follows. He will think of some prime number $p$ ($2\le p< 10^{10}$)...
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Four Square Description: Inspired by a Piet Mondrian painting, you want to make a four-pane window out of four colored rectangles of glass. You are given the sizes of the four panes of glass. Can you arrange them into a square? You may rotate the panes. The panes should cover the entire square without ...
27,728
Fractal Description: Fractals are really cool mathematical objects. They have a lot of interesting properties, often including: * fine structure at arbitrarily small scales; * self-similarity, i.e., magnified it looks like a copy of itself; * a simple, recursive definition. fine structure at arbitraril...
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Fractal Area Description: The $1^{\mathrm{st}}$ iteration in the construction of the CS Fractal consists of a single circle of radius $r > 0$. In the $2^{\mathrm{nd}}$ iteration, this “parent” circle spawns four “child” circles of radius $r/2$ that are tangent to the parent circle in each of th...
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Fractal Tree Description: A fractal tree $F_ i$ is defined in the following way. First, a rooted tree $F_0$ is given, which contains at least 2 vertices. $F_ i$ is then defined recursively in the following manner. Consider the set of vertices $S$ which are leaves in $F_{i-1}$. For each vertex $...
27,731
Fractional Lotion Description: Freddy practices various kinds of alternative medicine, such as homeopathy. This practice is based on the belief that successively diluting some substances in water or alcohol while shaking them thoroughly produces remedies for many diseases. This year, Freddy’s vegetabl...
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Framtíðar FIFA Description: Since you know the FIFA games only receive $k$ improvements every year, and you know you entered the FreezeChamber 9000 in the year 2022, you can determine what year it is. ## Input The input consists of two lines. The first line contains an integer $n$ ($0 \le n \le 2 \cdot 1...
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Framvindustika Description: Erla works at a software company that has recently received complaints from users. The users are unhappy with a specific operation in the software which has a long runtime. The users are uncertain whether the program is frozen or active after starting the operation. The code...
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Frankenstein's Monster Description: When Victor Frankenstein is not busy with his experiments, he likes playing chess, as it is, in his opinion, a symbol of human creativity and intelligent thought. In line with this, he likes teaching his creations, alive or not, how to play the game. Victor has been...
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Freckles Description: In an episode of the Dick Van Dyke show, little Richie connects the freckles on his Dad’s back to form a picture of the Liberty Bell. Alas, one of the freckles turns out to be a scar, so his Ripley’s engagement falls through. Consider Dick’s back to be a plane with freckles at variou...
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Free Desserts Description: Quido has lunch in Hugo’s restaurant every day. He likes the restaurant because all of its prices are expressed as integers, and for each possible price (i.e. $$1$, $$2$, $$3$, etc.) there is at least one beverage and at least one main dish on the menu. Every day there ar...
27,737
Free Food Description: Do you know what attracts almost any college student to participate in an event? Yes, free food. It doesn’t matter whether the event involves a long (sometimes boring) seminar. As long as free food is served for the event, then students will surely come. Suppose there are $N$ ...
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Free Goodies Description: Petra and Jan have just received a box full of free goodies, and want to divide the goodies between them. However, it is not easy to do this fairly, since they both value different goodies differently. To divide the goodies, they have decided upon the following procedure: the...
27,739
Free Solo Description: Alex is a climber who is planning his next free solo expedition. He wants to do a completely new climb this time, one that nobody else has done before. Before he starts the climb, he wants to get a rough idea of what the shortest path to the top is. In climbing, Alex uses his ha...
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Free Weights Description: The city of Bath is a noted olympic training ground—bringing local, national, and even international teams to practice. However, even the finest gymnasium falls victim to the cardinal sin…Weights put back in the wrong spots. All of the pairs of dumbbells sit in no particular orde...
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Free-Form Input Description: You are to read a sequence of lines and, for each line, compute the sum of the numbers on that line. Each line contains one or more numbers. Numbers are separated by commas. A number may be positive or negative (preceded by a minus sign), and may or may not contain a decima...
27,742
FreeCell Description: FreeCell Solitaire is, just as computer science, mostly about sorting. The goal is to sort a deck of cards using a fairly convoluted algorithm. The rules are the following: A shuffled deck is laid out in eight stacks. Only the topmost card of a stack may be moved. A card of value...
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Freight Train Description: The chemical company NS (Nasty Substances) has three factories: one in the Netherlands, one in Belgium and one in Luxembourg. Chemicals are moved between the factories on a regular basis, which is always done by freight train. Last night, the the weekly shipment of chemicals ...
27,744
French Fries Description: An infinite number of people are standing in a line, which extends infinitely to both left and right. $P$ different people are selected to get one French fry each. Since this is somewhat unfair, everybody simultaneously takes all their French fries and split them in two, givin...
27,745
Frenemies Description: Grogar was a legendary tyrant who once wreaked havoc across Equestria. Ages ago, his mythical bell and source of power was stolen and hidden at the top of the treacherous Mt. Everhoof, and he was forced to go into hiding. At long last, he has decided that the time is ripe for re...
27,746
Frequent Flier Description: An airline is offering a strange new rewards program to offer free flights to travelers. The program can be parameterized with two integers $m$ and $k$. Within any $m$ consecutive months, a traveler must pay for at least $k$ of those flights (if there are fewer than $k$ fli...
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Friday the 13th Description: Your task is to figure out how many times there will be Friday the 13th based on the calendar specifications. ## Input The first line of the input consists of a single integer, $T$, the number of test cases. The first line of each of the $T$ test cases is a line with two ...
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Fridge Description: The technology behind the fridge has changed little over the years. Even so, many of the original owners of the Fred W. Wolf domestic refrigerator of 1913 would be amazed by the size and features of the modern appliances. However, since the 1960s one thing has been common for all fr...
27,749
Friend of a Friend Description: Snark Muckleburg, CEO of renowned social network Friendface, wants to keep a close eye on how connected the users of his platform are. You have been assigned to write a monitoring program that tracks the connection status of every pair of users, namely whether they are F...
27,750
Friendly Fire Description: A typical scenario where the torpedoes will be used is a 2D plane, where the torpedo is fired from $(0,0)$ towards $m$ ships in the positive $y$-direction. Every ship has the form of a line segment parallel to the $x$-axis, with integer coordinate endpoints. The torpedo is sh...
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Friendly Interactive SHell Description: You might have heard about the friendly interactive shell - fish. It’s terminal based, but a bit friendlier to new users who can’t remember the commands they typed before. Fish can use your history of commands for command completion: pressing up (“^”) finds the l...
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Friendly Rivalry Description: The leaders of the International Coalition for Planetary Change (ICPC), a non-profit fighting for environmental awareness, are worried that their regional chapters are not doing enough to make a real impact on climate change. Inspired by the latest studies that competition...
27,753
Friends Description: High school is all about being in the coolest group of friends. Headmistress Umbridge knows this, and she also knows that knowledge is power. She has collected data on all of the $n$ students at the school, asking each of them who they are friends with. Now she has a list of re...
27,754
Friends Description: $N$ friends are playing a game. The game is played on a row of $L$ squares, numbered from $0$ to $L - 1$, where squares $i$ and $i+1$ are adjacent to each other. At most one friend stand on each square at any given time. In each step of the game, one friend jumps from its current s...
27,755
Frogger Description: “Frogger” was one of the first really popular arcade games after it was introduced by SEGA in 1981. The game consists of helping a frog cross a multi-lane motorway without getting run over by a car. You are given a view of an n-lane motorway where each lane consists of m different ...
27,756
Froggie Description: You are recreating the classic ‘Frogger’ video game. You do not need to worry about sprites, music, or animation (that is left to the game’s art team). Each level consists of a road with multiple lanes, with cars traveling in both directions. Cars within each lane are evenly-space...
27,757
From A to B Description: You are given two integers, $a$ and $b$. You want to transform $a$ to $b$ by performing a sequence of operations. You can only perform the following operations: * Divide $a$ by two (only if $a$ is even) * Add one to $a$ Divide $a$ by two (only if $a$ is ...
27,758
Frosh Week Description: During Frosh Week, students play various fun games to get to know each other and compete against other teams. In one such game, all the frosh on a team stand in a line, and are then asked to arrange themselves according to some criterion, such as their height, their birth date, ...
27,759
Frosh Week Description: Professor Zac is trying to finish a collection of tasks during the first week at the start of the term. He knows precisely how long each task will take, down to the millisecond. Unfortunately, it is also Frosh Week. Zac’s office window has a clear view of the stage where loud mu...
27,760
Frosting on the Cake Description: Iskander the Baker is decorating a huge cake, covering the rectangular surface of the cake with frosting. For this purpose, he mixes frosting sugar with lemon juice and food coloring, in order to produce three kinds of frosting: yellow, pink, and white. These colors ar...
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Frozen Rose-Heads Description: The winter is coming and all the experts are warning that it will be the coldest one in the last hundred years. Freddy needs to make sure that his garden does not sustain any damage. One of the most important tasks is to make sure that no water remains in his large wateri...
27,762
Fruit Baskets Description: Marek is a boss of a fruit company and he sometimes has crazy ideas. He wants to introduce a new product – fruit baskets. They will contain all possible combinations of fruits to satisfy different customer needs, but at most one piece of each fruit. He doesn’t want to have sm...
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Fruit Slicer Description: John introduces his game to his best friend Sean, who soon gets bored of playing the simple game. But as a teaching assistant of the algorithm course, Sean decides to turn the game into a homework assignment. He asks the students in the algorithms course to write a program tha...
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Frumtölur Description: Welcome to Forritunarkeppni Framhaldsskólanna! IF you have competed before you might know that the problem authors are smitten with primes. For you newcomers a brief description of prime numbers follows. An integer $N$ is considered to be prime if it can only be divided by $...
27,765
Frumtölutalning Description: Counting all the primes between $1$ and $100$ shows that there are $25$ prime numbers smaller than $100$. With a little more work one can show that there are $168$ prime numbers smaller than $1\, 000$. Given two integers, $a$ and $b$, count the number of primes sma...
27,766
Frustrated Queue Description: The toilet in Freddy’s garden is broken, so his only chance are public toilets nearby. One day, there is a long queue of people in front of the toilets. Freddy is in a big need and so he desperately wants the queue to be served as quick as possible. To use the toilets, yo...
27,767
Full Depth Morning Show Description: All boring tree-shaped lands are alike, while all exciting tree-shaped lands are exciting in their own special ways. What makes Treeland more exciting than the other tree-shaped lands are the raddest radio hosts in the local area: Root and Leaf. Every morning on FM ...
27,768
Full Tank? Description: After going through the receipts from your car trip through Europe this summer, you realised that the gas prices varied between the cities you visited. Maybe you could have saved some money if you were a bit more clever about where you filled your fuel? To help other tourists (...
27,769
Fullkomin mylla Description: Arnar and Hannes are very competitive friends and love competing with one another. They are always looking for new games to compete at and they both prefer games involving a lot of thinking. Hannes found a new version of tic-tac-toe called Fullkomin mylla and found it like...
27,770
Fun House Description: American Carnival Makers Inc. (ACM) has a long history of designing rides and attractions. One of their more popular attractions is a fun house that includes a room of mirrors. Their trademark is to set up the room so that when looking forward from the entry door, the exit door a...
27,771
Fun with Fibonacci Description: The Fibonacci sequence is defined by the following recurrence relation: $F_ n = F_{n - 1} + F_{n - 2}$, with seed values $F_0 = 0$ and $F_1 = 1$. The first few values of the Fibonacci sequence are $0, 1, 1, 2, 3, 5, 8, 13, 21, \ldots $ Let: * $G(1, n)$ denot...
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Functional Fun Description: A mathematical function is something that takes each object (like a number) from a set of possible values (called the domain), and produces a single object (again, perhaps a number) from another set of possible values (called the codomain). Functions can be defined over any ...
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Fundamental Neighbors Description: The fundamental theorem of arithmetic says that any natural number greater than one can be written uniquely as the product of prime numbers. For example: $3 = 3^1$, $4 = 2^2$, $6 = 2^1 \times 3^1$, $72 = 2^3 \times 3^2$, and in general, for prime numbers $p_1...
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Funny Games Description: Nils and Mikael are intergalaxial fighters. Now they are competing for the planet Tellus. The size of this small and unimportant planet is $1 < X < 500$ gobs. The problem is that their pockets only have room for one gob, so they have to reduce the size of the planet. They h...
27,775
Furry Nuisance Description: In order to protect himself from evil bunnies, Freddy decided to install an automatic system to detect them in pictures from surveillance cameras. Sophisticated software detects important points in the picture and lines between them. Unfortunately, the terrain in the picture...
27,776
Fuzzy Family Tree Description: Your friend Sue B. Tree, of the Rootingford Trees is facing a problem. Her clan of well-known algorithmic problem solvers has a large painting of their family tree hanging on the wall, tracing the lineage of the $N$ family members all the way back to Enar E. Tree himself,...
27,777
Fyrirtækjanafn Description: Hannes is working on his new startup company where his goal is to help other startup companies choose a good name. He has looked into several companies and thinks he has developed a formula that helps any company become a unicorn (reach a value of $\$ 1\, 000\, 000\, 000...
27,778
Färgrobot Description: A robot can move along a row of colored squares. Every square can be either red, green or blue. A command to the robot is a color. The robot responds by moving to the right until it stands on the color specified by the command. Write a program that, for a given sequence of square...
27,779
GCD Description: Given two integers $A$ and $B$, compute their greatest common divisor. ## Input The first and only line contains the integers $A$ and $B$ ($1 \le A, B \le 10^9$). ## Output Output a single integer – the greatest common divisor of $A$ and $B$. **Sample Input 1** **Sample Output 1*...
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GCD Harmony Description: Consider a tree with undirected edges, where each node has an integer value. Adjacent nodes are said to be GCD-harmonic if the greatest common divisor (GCD) of their values is strictly greater than $1$. You can modify the value of any tree node to any positive integer. The cost of...
27,781
GCD Pairs Description: In the Shape Galaxy, where all shapes are sentient beings, there is currently a feud between circles and squares. Circles want all pathways to be flat while squares argue that they should be evenly spaced inverted catenary shaped bumps. Because of this feud, circles have begun to...
27,782
GCD Sum Description: Given an integer $N$, compute the sum Here, $\gcd (i, j)$ is the greatest common divisor of $i$ and $j$, and $i \mid N$ denotes that $i$ is a divisor of $N$. ## Input The first and only line contains the integer $N$ ($1 \le N \le 10^{14}$). ## Output Output the sum in the task des...
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GCD Sum 2 Description: Given an integer $N$, compute the sum where $\gcd (i, j)$ denotes the greatest common divisor of $i$ and $j$. ## Input The first and only line contains the integer $N$ ($1 \le N \le 5 \cdot 10^7$) from the statement. ## Output Output the sum from the task description. **Sample ...
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GCD and LCM Description: It is known that the greatest common divisor of two integers $a$ and $b$ is $x$, and that their lowest common multiple is $y$. Given $x$ and $y$, determine all possible pairs $(a, b)$. ## Input The first and only line contains the integers $x$ and $y$ ($1 \le x, y \le 10^...
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GCDs Description: Given a sequence $A$ of $n$ numbers, define $f(lo,hi)$, $1 \le lo \le hi \le n$, as the Greatest Common Divisor of all the numbers $A_{lo}$ through $A_{hi}$, inclusive. Note that $lo$ and $hi$ are indices, not members of the list. Given an array, considering all possible values of...
27,786
GCVWR Description: You are looking to buy a new camper, but you are a bit concerned that your truck might not be able to safely pull the camper you are currently interested in purchasing. So you do some calculations. First, you look up your truck’s Gross Combined Vehicle Weight Rating (GCVWR); the max...
27,787
GME Stonks Description: Elon Fusk wants to make stonks on the stock market, so he decides that he will trade some GME stocks today. Mr. Fusk is very active on Twitter. Immediately after performing any trade he will tweet about it. His large Twitter following pays great attention to his tweets which causes...
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GMO Description: A multinational company is asking you to help them genetically modify an apple. In order for the apples to grow faster, to get more of them, to make them bigger and make them look nicer and more symmetrical, the apple’s DNA requires an insertion of a certain swine gene. The apple’s DN...
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GREAT + SWERC = PORTO Description: We want to have a great SWERC at Porto this year and we approached this challenge in several ways. We even framed it as a word addition problem, similar to the classic $SEND+MORE=MONEY$, where each letter stands for a single digit (0, 1, 2, ..., 8, 9) that makes the a...
27,790
Gaggle Description: Rather than having managers overseeing the work, the main method used to coordinate work at Gaggle is a mentor system: each Gaggler designates some other Gaggler as their mentor, with whom they discuss their ongoing projects. This mentor relation may or may not be symmetric (in othe...
27,791
Gagnaleki Description: A hacker broke into Forritun.is and leaked several gigabytes of data onto the wider internet, including registration info for contestants of Forritunarkeppni Framhaldsskólanna from all years. In this data there is among other things the username and password from you and other co...
27,792
Galactic Collegiate Programming Contest Description: This year there are $n$ teams in the contest. The teams are numbered $1,2,\ldots ,n$, and your favorite team has number $1$. Like today, the score of a team is a pair of integers $(a,b)$ where $a$ is the number of solved problems and $b$ is the tota...
27,793
Galactic Sabotage Description: Pichuu has just finished his catching spree in the safari zone and decided to spend the day organising his messy PC, where his Pokemon are stored. A PC has multiple boxes in a row and each box can store an unlimited amount of Pokemon. For simplicity, you can assume that t...
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Galactic Warlords Description: Will the galaxy see peace at last? All the warlords have gathered to divide all of space between themselves. The negotiations have come quite far and the warlords have finally agreed on a peaceful way of deciding who gets what. The $2$-dimensional galactic map must fi...
27,795
Galaksija Description: A long time ago in a galaxy far, far away, there were $N$ planets. There were also $N - 1$ interplanetary paths that connected all the planets (directly or indirectly). In other words, the network of planets and paths formed a tree. Additionally, each path was enumerated ...
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Galaxy Quest Description: You are travelling through the galaxy in your spaceship. There are $n$ planets in the galaxy, numbered from $1$ to $n$ and modelled as points in $3$-dimensional space. You can travel between these planets along $m$ space highways, where each highway connects two planets along...
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Gallup Description: Often, we see results of gallups, like this: * Prefer red: 3.5% * Prefer green: 4.5% * Prefer yellow: 22.0% * Prefer blue: 70.0% Prefer red: 3.5% Prefer green: 4.5% Prefer yellow: 22.0% Prefer blue: 70.0% and you begin to wonder: how many people did they really ask? If the numbers are ...
27,798
Gambling Game Description: The Ionian Commission on Procuring Cash has come up with a new gambling game to raise funds for the government. The game is played as follows: Each week, the government will televise a set of $m$ balls (numbered $1 \ldots m$) being selected one at a time without replaceme...
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