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Game Design Description: Carol enjoys playing with wooden games. The objective of the game that fascinates her the most is to tilt a maze, made out of $1\text { cm}$-by-$1\text { cm}$ blocks, in any of the four cardinal directions to move a ball to a hole in the centre at $(0, 0)$. As shown in Figu...
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Game Night Description: It is finally Bobby’s birthday, and all of his Acquaintances, Buddies and Colleagues have gathered for a board game night. They are going to play a board game which is played in up to three big teams. Bobby decided to split his guests into groups based on how well he knows them:...
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Game Rank Description: Each rank has a certain number of “stars” that one needs to gain before advancing to the next rank. If a player wins a game, she gains a star. If before the game the player was on rank $6$-$25$, and this was the third or more consecutive win, she gains an additional bonus star fo...
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Game Scheduling Description: The playing schedule should be divided into rounds. A player can play at most one game per round. If a player does not play a game in a round, that player is said to have a bye in that round. Your task is to write a program that constructs a playing schedule so that no pla...
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Game Show Elimination Description: You are running an elimination-style game show, where players are eliminated one at a time until only one remains. Based on what you know about the contestants, you are trying to predict the results. Each week, the remaining contestants take part in a competition, wh...
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Game Strategy Description: Alice and Bob are playing a board game. The board is divided into positions labeled $a, b, c, d, \dots $ and the players use a gamepiece to mark the current position. Each round of the game consists of two steps: * Alice makes a choice. Depending on the current position, ...
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Game Suggestions Description: Khadija is working on her new game, which will be a…well, she doesn’t really know yet! She has made an extremely flexible game engine, and being a skilled developer, she can implement just about anything in it. To find out what the game should contain, she has asked her f...
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Game Theory Description: SoCCat challenges you to the following game: There are $n$ cells arranged in a row, with numbers $1$ to $n$ written on them. The $i$-th cell from the left has the number $p_ i$ written on it. SoCCat also has another array $a$ of size $n$. Before the game begins, SoCCat will place...
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Game of Cards Description: Alice and Bob created a new game while at the beach this summer. All they need is a set of numbered playing cards. They start by creating $P$ piles with all cards face-up and select a non-negative number $K$. After that, they take turns like this: * A player starts by se...
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Game of Dice Description: if you have $k$ ones, you get $k$ points. if you have $k$ twos, you get $2k$ points. if you have $k$ threes, you get $3k$ points. if you have $k$ fours, you get $4k$ points. if you have $k$ fives, you get $5k$ ...
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Game of Divisibility Description: Viet and Nam are playing a game set up with a list of $n$ positive integers $a_1, a_2, \ldots , a_ n$ and a positive integer $k$. Two players alternatively take turns removing a number from the list until the list is empty. The final score of each player is the sum...
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Game of Gnomes Description: You have $n$ gnomes at your disposal. Before the battle, they must be divided into at most $m$ non-empty groups. The battle will then proceed in turns. Each turn, your gnomes will attack the enemy, causing one unit of damage for each living gnome. Then the enemy will att...
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Game of Throwns Description: Daenerys frequently invents games to help teach her second grade Computer Science class about various aspects of the discipline. For this week’s lesson she has the children form a circle and (carefully) throw around a petrified dragon egg. The $n$ children are numbered fro...
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Gameworld Tornado Description: The Brilliant Game Overseers (BGO) is building a brand new game. The investors have noted that large gameworlds is a selling point these days, so in order to appease the them, a large gameworld with lots of interesting activities has been planned. In addition to a large m...
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Gandalf's Spell Description: Today, Gandalf woke up from an awful dream that told him that the hobbit needs to be mentally prepared for the journey ahead. So, Gandalf decided to create a spell where it would replace every unique word in a sentence with a unique character. However, Gandalf is cheeky so ...
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Gangur Description: ## Input The input consists of a single line describing the contents of all the section of the hallway. The hallway is at least $1$ section and at most $10^6$ sections. If the hallway is described by > then there is a person there facing right. If the hallway is described b...
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Garage Door Code Description: There have been an increasing number of laptop thefts in your area lately. After yours was recently stolen, too, you decided that you had enough and are going to do something about it! After asking around, you heard some rumors about where the stolen laptops have been hidd...
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Garbage Tracking Description: Talulla has been hired to fix an issue for Sgudal Cleaning - a company that specialises in making garbage cleaning robots for the city New Glasgow. Instead of collecting garbage from the streets, the cleaning robots now dump garbage instead! In fact, the cleaning robots no...
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Garden Decorations Description: Every day when going to school and back home, Detje walks along a street with $N$ houses, numbered from $0$ to $N-1$. Currently, house $i$ is inhabited by person $i$. For a change of scenery, the residents have decided to switch houses with each other. The pe...
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Garden of Thorns Description: Eddy owns a rectangular garden and has noticed some trespassers stomping through his garden. There are some plants that he wants to protect. He hires an assistant, Zyra, to patrol and protect his garden. Zyra cannot be bothered to monitor his garden, so she plants a circl...
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Gas Station Description: You are a late night attendant at a busy gas station. You can only go home after all the cars have topped up their fuel tanks and left the gas station. The gas station you work at has $P$ gas pump columns, counting from left to right, and each column has two gas pumps, pump...
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Gas Station Numbers Description: Many gas stations use plastic digits on an illuminated sign to indicate prices. When there is an insufficient quantity of a particular digit, the attendant may substitute another one upside down. The digit “6” looks much like “9” upside down. The digits “0”, “1” and “8...
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Gasqutvå Description: Gasquen is antiquated so Gasqutvå shall now be crowdfunded by the Chalmers students. The $N$ students communicate along a tree where the students are nodes. Students are arbitrarily numbered from $1$ to $N$. The $i$th student’s generosity is described by one integer $a_ i$. Yo...
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Gathering Description: In order to draw more support and make their unhappiness known to the municipality, a group of citizens has agreed to gather at an intersection of the city to protest. The question is: which intersection? Since there is not much difference between them, the idea was raised to sel...
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Gathering in Yorknew Description: Hunters from all over the world are gathering in Yorknew — where the ‘International Hunter Programming Contest $2020$’ will take place. As Gon has previously passed the final round of Hunter Exam and became a Hunter, you may be able to see Gon in Yorknew! There is...
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Gatnamót Description: The police in Squareland is chasing criminals. The crime was commited at an intersection at the coordinates $(0, 0)$ and the police has received an anonymous tip on the criminals’ location. The tip was that the criminals are situated at some intersection within $r$ kilometers from...
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Gauntlet of Fire Description: Spike is competing in the Gauntlet of Fire for the title of Dragon Lord. To succeed, he needs to traverse the labyrinthine volcanic tunnels, avoiding the treacherous elements and making it from chamber to chamber as quickly as possible. The cave has $N$ chambers and $M$ t...
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Gauss Squares Description: You are given a prime $p$ satisfying $p = 1 \pmod{4}$ and should print non-negative integers $x, y$ satisfying $p = x^2 + y^2$. ## Input The first and only line of input contains a prime $p \leq 10^{18}$ which satisfies $p = 1 \pmod{4}$. ## Output Print two non-ne...
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Gear Changing Description: Lucy is making her road bike ready for the season. All parts have been checked for wear and tear and washed clean and she is ready to put the beauty back together again. There is only one thing troubling her. During the winter she has been to several motivational talks by pre...
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Gear Wheels Description: Gear wheels can be connected to form chains, where the teeth of adjacent gears interlock. This helps to transmit rotary motion over a long distance. Now, you have $N$ gear wheels arranged on a straight line, numbered from $1$ to $N$ from left to right. Gear wheel $i$ has $T_ i...
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Gears Description: A set of gears is installed on the plane. You are given the center coordinate and radius of each gear, which are all integer-valued. For a given source and target gear, indicate what happens to the target gear if you attempt to turn the source gear. Possibilities are: * The source g...
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Gears and Axles Description: You have an assortment of circular gears with varying numbers and sizes of teeth. You also have a motor that spins at one revolution per second, as well as an unlimited number of (identical, arbitrarily long) axles. The motor and all gears fit the axles, and everything atta...
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Gears in Action Description: Peter works in the Slovak Institute of Gears. After years of hard work he has constructed a special machine whose only purpose is to rotate a lot of gears. After watching it for three hours (it makes a good mechanical "screensaver"), he got interested in one mathematical pr...
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Geezer Scripts Description: The other day Unnar was playing the video game Geezer Scripts, Geezer Scripts V to be precise. He opened a door (in the game) and before he knew he was in a large and complicated cave-system, full of enemies who will attack as soon as Unnar gets to close to them. What’s wors...
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Geimskip Description: “A long time ago, in a galaxy far, far away…” The rebels have finally found the location of the new Death Star and hope to perform an all out attack under the leadership of General Gial Ackbar. Ackbar has committed all of their ships, the ships being MC80 starships, CR90 corvettes, D...
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Gem Island Description: Gem Island is a tiny island in the middle of the Pacific Ocean. Until recently, it was known as one of the poorest, but also most peaceful, places on Earth. Today, it is neither poor nor peaceful. What happened? One sunny morning, not too long ago, all inhabitants of Gem Island...
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Gene Block Description: You discovered that you could easily trade a big dirt block of size $N$ for one of the rarest Minecraft blocks, Gene. Although excessively abundant, dirt blocks in this server come in different sizes — and, after careful observation, you realized that the size of each indivi...
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Gene Folding Description: International Cell Processing Company (ICPC) is a world leader in the analysis of genetic sequences. A genetic sequence is a sequence of nucleotides, which in this problem is represented by a string containing only the letters A, C, G, and T in some combination, each letter re...
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Genealogical Research Description: ## Input Your program accepts a series of commands, one per line. The commands are described by the following syntax: ``` command ::= birth ::= death ::= ancestors ::= descendants ::= QUIT birth ::= BIRTH child : date : mother...
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Generalized FizzBuzz Description: FizzBuzz is a common coding interview problem. The problem is as follows: Given a positive integer $n$, for all integers $i$ from 1 to $n$, inclusive: * If $i$ is divisible by both $3$ and $5$, print "FizzBuzz". * Otherwise, if $i$ is divisible by $3$, print "Fizz". * ...
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Generalized Knights Description: On an infinitely large grid, a generalized knight stands at position $(0, 0)$. The knight is allowed to move in $8$ ways. First, it may move either $\pm a$ or $\pm b$ steps horizontally, and then $\pm a$ or $\pm b$ steps vertically. Compute the minimum number of moves ...
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Generalized Recursive Functions Description: You have been employed by the math department to find the solutions to different recursive, integer-valued functions. Every function is of the form: where all parameters $a_ i, b_ i, c, d$ are non-negative integers, and for each $i$, $a_ i+b_ i > 0$. Write ...
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Generating Numbers Description: Ging is working on the next generation of computers – ‘Tanquum computers’. ‘Tanquum computers’ take advantages of advanced Physics, allowing them to rearrange the digits of every positive integer in one instruction. The application is limitless. For example, from number ...
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Generators Description: The volcanic island of Fleeland has never had a proper electric net, but finally the administration of the island have agreed to build the island’s power plants and network. On the island’s coast are its $n$ cities. The administration has surveyed the cities and proposed $m$ of the...
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Genetic Reconstruction Description: You’re in charge of studying a new species, and you’d like to make sure the work that you’ve collected is correct. There are several creatures. For each one, you know the eye color they have. This is denoted by one of the first $20$ English lowercase letters (from ‘...
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Genetic Search Description: Technology has greatly changed the field of biology in the last decade, since biological information can be digitized and analyzed by computer. One of the most basic analysis tasks is counting the number of occurrences (or near-occurrences) of a search string $S$ inside ...
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Genetics Description: A colony of alien bacteria has recently been discovered close to a crater in New Mexico. Dr. Poucher is in charge of the scientific team at the ICPC BioLab committed to the study of the alien DNA structure. We briefly sketch their discoveries here. Alien DNA molecules have the st...
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Genetics Description: For villains that intend to take over the world, a common way to avoid getting caught is to clone themselves. You have managed to catch an evil villain and her $N-1$ clones, and you are now trying to figure out which one of them is the real villain. To your aid you have each person’s...
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Genijalac Description: Mirko is a genius. But the purpose of his inventions is not always obvious. His latest invention, the Shuffle-o-matic 3175, is one of those. The Shuffle-o-matic is used in a very special way. First Mirko places $N$ paper cards, with numbers 1 to $N$ printed on them, on the Sh...
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Genius Description: If someone were to make a prediction that everyone thought was doomed to failure, and it turned out to be correct, wouldn’t it be shortsighted simply to dismiss this as a stroke of luck? What if the person could do so over and over again? Instead of explaining away those capable of ...
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Geometric Gridlock Description: Pentominous is a grid logic puzzle based on the twelve pentominoes. A pentomino is a polygon formed by connecting five equal-sized squares edge to edge. The goal of this puzzle is to divide a grid into regions of size $5$ (that is, pentominoes), so that no two regions t...
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Geometry is Fun Description: Geometry is Fun! Won’t you agree? From the Greeks to the Chinese, and to you, we all love geometry! It so happens that The Great Lord Pooty loves geometry as well! So here is a geometry question for you. You have been hit by a truck and reincarnated as a point in a 2-dimen...
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George Description: Last week Mister George visited Croatia. Since Mister George is a very important person, while he was in a street, the police disallowed entry to that street, but vehicles that entered the street before Mister George could continue driving. While Mister George was visiting, Luka dr...
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Geppetto Description: Everyone’s favorite character and puppet-maker Geppetto has opened a new pizza place, the best in town. Geppetto is trying to make the best pizza possible, but at the same time he doesn’t want to have a small selection of pizzas. He makes his pizzas out of $N$ ingredients marked with...
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Gerrymandering Description: Electoral systems across the world can vary widely. In some systems, such as winner-take-all, the winner is determined by the plurality of votes—the candidate that receives the most votes wins, and the loser(s) do not get a position. Such elections can have “wasted votes.” ...
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Get Off My Lawn! Description: Tom the Straight Builder has finally finished building his Great Wall. Being a Straight Builder he has of course built a wall with no bends in it at all. And as far as you can see he has built this wall infinitely long and infinitely thin. On one side of the wall Tom’s wife E...
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Get Shorty Description: Nils and Mikael are intergalaxial fighters as well as lethal enemies. Now Nils has managed to capture the poor Mikael in his dark dungeons, and it is up to you to help Mikael escape with as much of his pride intact as possible. The dungeons can be viewed as a set of corridors and ...
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Get a Clue! Description: Developed in the 1940s in the United Kingdom, the game of Cluedo is one of the most popular board games in the world. The object of the game is to determine who murdered Mr. Body, which weapon was used to murder him, and where the murder took place. The game uses a set of cards...
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Get to Work Description: You work for a company that has $E$ employees working in town $T$. There are $N$ towns in the area where the employees live. You want to ensure that everyone will be able to make it to work. Some of the employees are drivers and can drive $P$ passengers. A capacity of $...
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Get-Rich-Quick Schemes Description: Cashback means that you earn a certain percentage of cash back on purchase you make, depending on the type of purchase. Formally, there are $n$ categories of merchandise. If you purchase merchandise from category $i$ for $x$ SEK, you earn $p_ i \cdot x$ SEK b...
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Getting Gold Description: We’re building an old-school back-to-basics computer game. It’s a very simple text based adventure game where you walk around and try to find treasure, avoiding falling into traps. The game is played on a rectangular grid and the player gets very limited information about her ...
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Getting Rid of Coins Description: When Per was living in New York, he couldn’t use his debit card as often as in Sweden. He had to carry cash all the time and his wallet was getting heavy from all the coins he was carrying around. He was once in a candy store buying a few kilos of candy and he wanted t...
27,861
Getting Through Description: A long and straight corridor is fitted with a number of sensors. Each sensor has a certain range within which it can detect objects or persons. If a part of an object is within the sensor’s range, an alarm will go off. Otherwise, nothing will happen. Ethan needs to travers...
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Getting a Jump on Crime Description: Your friend Robin is a superhero. When you first found out about this, you figured “everybody needs a hobby, and this seems more exciting than stamp collecting,” but now you are really thankful that somebody is doing something about the crime in your hometown. Ever...
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Ghost Leg Description: A Ghost Leg is a method for representing permutations. A Ghost Leg can be represented as a set of vertical lines, each line corresponding to one element of the set being permuted. Horizontal lines (like the rungs of a ladder) connect adjacent vertical lines in such a way that no...
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Ghostbusters Description: The Bureau of Approved Peripherals for Computers (BAPC) is designing a new standard for computer keyboards. With every new norm and regulation, hardware becomes obsolete easily, so they require your services to write firmware for them. A computer keyboard is an array of $M$ rows ...
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Ghostbusters 2 Description: In the 1984 Ghostbusters™ movie, the protagonists use proton pack weapons that fire laser streams. This leads to the following memorable dialog between scientists Peter Venkman and Egon Spengler: Spengler: There’s something very important I forgot to tell you. Venkman: What...
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Ghostbusters 3 Description: There is something strange in the neighbourhood. Who you gonna call? Ghostbusters! A number of ghosts have decided to roam the street, and the Ghostbusters have arrived to deal with this situation. Luckily all the ghosts have decided to stay on one side of a very long stree...
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Gig Combinatorics Description: Given the hype rating of each of Tóti’s songs in the order he wrote them, how many setlists can he make? ## Input The first line of input consists of an integer $n$ ($1 \leq n \leq 10^6$), the number of songs Tóti has written. The second line consists of $n$ integers, each ...
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Gin Fizz Description: The classic Gin Fizz is the best-known cocktail in the fizz family, a mixed drink variation on the older sours family of cocktails. Their defining feature is an acidic juice (in this case, lemon) and carbonated water. The Gin Fizz appears first in Jerry Thomas’s classic The Bar-Te...
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Gin and Tonic Description: It’s time once again for the annual gathering of the Club of Allergic Tonic Tasters in Scrollbar (CATTIS). Club members with various rare allergies come together to sample a range of delicious tonic-based beverages. This year’s theme centers around the timeless highball cockt...
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Ginger Candy Description: Mr. G is one of the most excellent students in North River High School for Gifted Students. Despite having impressive performance in a programming competition and making it to the next round, he was not totally happy since his best friend did not get such a great achieveme...
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Gini Stuðull Description: Here $\lvert x\rvert $ denotes the absolute value of $x$: $\lvert x\rvert = x$ if $x \geq 0$, but $\lvert x\rvert = -x$ if $x < 0$. ## Input The first line of the input contains one integer $n$, the number of individuals in the group. Then there will be $n$ lines, one for each i...
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Girðingaherping Description: A fence has been placed around the perimeter where a new building will be constructed. However, news have spread of budget cuts that are coming up, so the area for the building has to be made smaller. The mathematicians that were on call said that contractions work great fo...
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Giskaðu á svarið Description: ## Input There is no input. ## Output An integer between $0$ and $1000$. ## Explanation of Sample Inputs In the sample the number $500$ is printed. A solution print ing the number $500$ gets $0$ points, because it is far from the answer. ## Scoring If $X$ is the dis...
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Git Good Description: Doris’s younger brother Boris has recently started working as a programmer at E-Max (an online hamburger chain). Like all major companies, E-Max uses the version control system git to save changes to the codebase. Unfortunately, Boris hasn’t learned git yet and needs help! When s...
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Gladiators Description: In the TV game show Gladiators, the final competition is to run through a steeplechase course. To get some variation, the producer has decided to change the course each week. The course is always built out of m obstacles, all of different heights, placed along a straight line. A...
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Glasses Foggy, Mom's Spaghetti Description: Conway’s glasses are foggy, Knees weak, arms are heavy. Palms are sweaty, mom’s spaghetti. He’s nervous, but on the surface he looks calm and ready to go home neat and tidy, but the streets are trippy. In order to go home, Conway needs to follow the street s...
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GlitchBot Description: One of our delivery robots is malfunctioning! The job of the robot is simple; it should follow a list of instructions in order to reach a target destination. The list of instructions is originally correct to get the robot to the target. However, something is going wrong as we upl...
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Global Warming Description: This is a very exciting week for John. The reason is that, as a middle school teacher, he has been asked to dedicate the entire week to teaching his class of $n$ students about the cause and effect of global warming. As John is very passionate about his planet, he’s going to...
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Glossary Arrangement Description: In Unix based operating systems, one of the most frequently used commands is ls, which displays a list of all the files in a directory in lexicographic order. In the most basic form, ls prints each filename on a separate line, but to improve readability and save sc...
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Glued Grid Description: A sliding puzzle consists of square tiles on a rectangular grid. Exactly one of the grid positions is empty, so that you can move the tile above, below, to its left, or to its right into the empty square and back. Each tile is labelled with a unique number, as shown in Figure 1...
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Gluttonous Goop Description: As a prominent researcher in the laboratorium for Breathtaking Agriculture through Petri dish Cultivation, you keep on looking for new organisms that might be the food of the future. Recently you have discovered a new fungus-type organism that seems to be nutritious and ver...
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Glyph Recognition Description: You are an archaeologist working at an excavation site where your team has found hundreds of clay tablets containing glyphs written in some ancient language. Not much is known about the language yet, but you know that there are only six different glyphs, each of them in t...
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Glötuð Gildi Description: The universities of Iceland have decided to host a large Nim tournament. Exactly $n$ teams have registered, and each team will compete exactly once against every other team. As is well known there are no ties in Nim, so in each game there is exactly one winning team which ...
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Gnoll Hypothesis Description: You are a huge fan of the RPG The Eldest Scrolls: Earthrim and know all of the game’s internal mechanics. For instance, when spawning a new monster, each of the $n$ different types of monsters in the game has some fixed probability of appearing, and you know exactly wh...
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Go with the Flow Description: In typesetting, a “river” is a string of spaces formed by gaps between words that extends down several lines of text. For instance, Figure 1 shows several examples of rivers highlighted in red (text is intentionally blurred to make the rivers more visible). Celebrated riv...
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Goat Rope Description: You have a fence post located at the point $(x, y)$ in the plane, to which a goat is tethered by a rope. You also have a house, which you model as an axis-aligned rectangle with diagonally opposite corners at the points $(x_1, y_1)$ and $(x_2, y_2)$. You want to pick a length...
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Goat Ropes Description: A farmer has $n$ goats. Coincidentally, he also has $n$ fixed posts in a field where he wants the goats to graze. He wants to tie each goat to a post with a length of rope. He wants to give each goat as much leeway as possible – but, goat ropes are notorious for getting tang...
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Goblin Garden Guards Description: In an unprecedented turn of events, goblins recently launched an invasion against the Nedewsian city of Mlohkcots. Goblins—small, green critters—love nothing more than to introduce additional entropy into the calm and ordered lives of ordinary people. They fear little,...
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God Save the i-th Queen Description: Did you know that during the ACM-ICPC World Finals a big chessboard is installed every year and is available for the participants to play against each other? In this problem, we will test your basic chess-playing abilities to verify that you would not make a fool of...
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Godzilla Description: Godzilla is rampaging through Tokyo again. Luckily, the Superior Defender Mech Force (SDMF) has sent its mech units to stop Godzilla’s attack. Mech units are gigantic bipedal robots, usually piloted by Japanese teenagers, that carry weapons of superior destruction. The weapons are...
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Going Dutch Description: You could each take all the receipts showing that someone paid something for you, and then pay that person back. But then you would need a lot of transactions, and you want to keep up the lazy spirit from your trip. In the end, it does not matter who transfers money to whom; as...
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Going in Circles Description: Hercule thought for a moment. “That is most peculiar,” he said. “But I may be able to help you.” He reached over and grabbed the lamp from the side table. “You see, each train carriage has a light switch like this one. By moving between the carriages and toggling these swi...
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Going to School Description: Cissi is walking from her home to school, following a long street going from the west to the east. On her way, she passes a number of street crossings where the crossing street either goes north (N), south (S) or both (B). At every street crossing, there are crosswalks on b...
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Going to Seed Description: The Great Seedling is a mythical spirit that supposedly rewards whoever catches it with farm crops that remain in bloom forever. Rumor has it that in the dead of tonight, it will be coming to Sweet Apple Acres—the Apple family’s farm! Applejack and Apple Bloom are hoping to catc...
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Gokigen Naname Description: Gokigen Naname is a Japanese puzzle game played on a square grid in which numbers in circles appear at some of the intersections on the grid. The objective is to draw diagonal lines in each cell of the grid, such that the number in each circle equals the number of lines ext...
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Gold Bandits Description: In the hills of a distant land there is a valley with many villages. The villages are all ruled by a cruel king who demands that each village pay him tribute in gold each year. The villages are required to bring gold to the king as quickly as possible when he demands it. Ther...
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Gold Leaf Description: Gold Leaf is a very thin layer of gold, with a paper backing. If the paper gets folded and then unfolded, the gold leaf will stick to itself more readily than it will stick to the paper, so there will be patches of gold and patches of exposed paper. Note that the gold leaf will a...
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Goldbach's Conjecture Description: The goal of this program is to find all unique ways to represent a given even number as the sum of two prime numbers. A prime number is an integer greater than $1$ that is evenly divisible by only itself and $1$. The first few prime numbers are $2$, $3$, $5$, $7$,...
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