Split (1)

train · 39.1k rows

task stringlengths 0 154k	__index_level_0__ int64 0 39.2k
The Big Painting Description: Samuel W. E. R. Craft is an artist with a growing reputation. Unfortunately, the paintings he sells do not provide him enough money for his daily expenses plus the new supplies he needs. He had a brilliant idea yesterday when he ran out of blank canvas: “Why don’t I create...	30,100
The Biggest Triangle Description: Three infinite lines define a triangle, unless they meet at a common point or some of them are parallel. Given a collection of infinite lines, what is the largest possible perimeter of a triangle defined by some three lines in the collection? ## Input The first line of ...	30,101
The Board Game Description: Ann-Charlotte and Berit have invented their own board game. The game is played with a board of size $N \times M$ and a chainsaw, and is intended for two players. The players take turns making a move until one of them cannot make a move, that player loses. A move works the fo...	30,102
The Bookcase Description: Wondering how small his bookcase could be, he models the problem as follows. He measures the height $h_ i$ and thickness $t_ i$ of each book $i$ and he seeks a partition of the books in three non-empty sets $S_1,S_2,S_3$ such that $\left(\sum _{j=1}^3 \max _{i \in S_ j} h_ i \righ...	30,103
The Brick Stops Here Description: You have been hired by several clients of a factory that manufactures brass bricks. Brass is an alloy of copper and zinc; each brick weighs $1000$ grams, and the copper content of a brick can range from $1$ to $999$ grams. (Note that brass with less than 55% or more th...	30,104
The Bus Card Description: You are going to purchase a bus card. It’s a refillable card that cash can be deposited into, and then used to ride the bus until you are out of money. You know that you’re planning to travel for $K$ Swedish crowns (SEK). Charging the card takes some time since you can onl...	30,105
The Calculator Description: Rumors are circulating that your school-provided calculator can be upgraded using a secret code. You’ve heard that if you can get the calculator to display the secret kålnami code on its screen and then press the equals sign, the calculator will unlock several secret mathema...	30,106
The Calculus of Ada Description: While mostly known for the programs she wrote for Charles Babbage’s Analytic Engine, Augusta Ada King-Noel, Countess of Lovelace, described how the method of finite differences could be used to solve all types of problems involving number sequences and series. These tec...	30,107
The Citrus Intern Description: The summer is closing in and you have set your eyes on a summer internship with your favourite fruit confederacy, Citrus. What you really want is to take over the entire organisation on your way to world fruit domination, but getting an internship is a nice first step. Y...	30,108
The Clock Description: When someone asks you what time it is, most people respond “a quarter past five”, 15:29 or something similar. If you want to make things a bit harder, you can answer with the angle from the minute hand to the hour hand, since this uniquely determines the time. However, most p...	30,109
The Colonization of El-gă-rizm Description: The mythical planet, El-gă-rizm, comprises $m$ islands surrounded by water. There are $n$ different natural resources to be found at various locations on the islands. Interestingly, each of the $n$ natural resources is present on exactly two islands; thus the...	30,110
The Coloring Game Description: Slugas Fulacek has challenged Oskar to a coloring game played on a paper with lots of circle on it. Some pairs of circles are connected by line segments, and are called friends. The players take turns coloring a circle that has not yet been colored. The player who moves ...	30,111
The Components Game Description: Narwhy the Narwhal likes playing games on his waterproof phone. Recently, he downloaded a new game from the OceanStore. It involves a rectangular grid made of white and black squares. After going through the tutorial, he learned that by touching any column it turns that...	30,112
The Cost of Speed Limits Description: By the year 3031, the ICPC has become so popular that a whole new town has to be built to house all the World Finals teams. The town is beautifully designed, complete with a road network. Unfortunately, when preparing the budget, the town planners forgot to take in...	30,113
The Council Description: Today is the day of the octennial meeting of the Council of Atrebla. To start off the meeting, the Council members spent sixteen minutes throwing darts as a means to quantify the intrinsic value of each town in Atrebla as a single integer. With this information the Council inte...	30,114
The Dark Chambers of Chalmers Description: You are on your way to the final competition of the Swedish Olympiad in Informatics, which is hosted at Chalmers Technical University. However, you have gotten lost in the university basement. Your sense of direction is not great, and what makes matters worse ...	30,115
The Darkness Description: Night clubs aren’t what they used to be. Our benevolent state has decided that, for health and safety reasons, every club must now meet a minimum lighting standard. They have moved to verify standards by dividing each club up into $1\text { m}^2$ cells and measuring the light ...	30,116
The Deal of the Day Description: A bored technician whose job requires inspecting each of $10$ equipment stations on a regular basis has tried to inject a little variety into his days by creating a deck of cards, each card bearing a number in the range $1..10$. From this deck he randomly deals out ...	30,117
The Dragon and the Knights Description: The Dragon of the Wawel Castle, following the conflict with the local Shoemakers’ Guild, decided to move its hunting grounds out of Kraków, to a less hostile neighborhood. Now it is bringing havoc and terror to the peaceful and serene Kingdom of Bytes. In the Ki...	30,118
The Dragon of Loowater Description: Once upon a time, in the Kingdom of Loowater, a minor nuisance turned into a major problem. The shores of Rellau Creek in central Loowater had always been a prime breeding ground for geese. Due to the lack of predators, the geese population was out of control. The peopl...	30,119
The Easiest Problem Is This One Description: Some people think this is the easiest problem in today’s problem set. Some people think otherwise, since it involves sums of digits of numbers and that’s difficult to grasp. If we multiply a number $N$ with another number $m$, the sum of digits typically change...	30,120
The Elk Description: You are in a forest. In this forest there is also a pair of elks - a cow (an adult female) and her calf (child). As most people know, it is dangerous to get between a cow and her calf, but it is not always clear how to avoid it. We model our forest as consisting of $N$ locations, and ...	30,121
The Embarrassed Cryptographer Description: What Odd Even did not think of, was that both factors in a key should be large, not just their product. It is now possible that some of the users of the system have weak keys. In a desperate attempt not to be fired, Odd Even secretly goes through all the users...	30,122
The End of the World Description: Legend says that there is a group of monks who are solving a large Towers of Hanoi puzzle. The Towers of Hanoi is a well-known puzzle, consisting of three pegs, with a stack of disks, each a different size. At the start, all of the disks are stacked on one of the pegs,...	30,123
The Ending of the End - Part 1 Description: Rarity: “Go, Twilight! Get help!” Applejack: “We’ll hold ‘em ‘til you get back!” Twilight Sparkle: “No! I can’t leave you here!” Fluttershy: “It’s our only chance!” Rainbow Dash: “You’ll come up with something to save the day!” Pinkie Pie: “You alway...	30,124
The Ending of the End - Part 2 Description: Previously... Twilight Sparkle: “No! I can’t leave you here!” Fluttershy: “It’s our only chance!” ...soon, all of Equestria will fall. Twilight Sparkle needs to make her way to the Crystal Empire to warn them and get help. The route is deadly; with ...	30,125
The Escape Description: You have all heard of the story of the three little pigs. However, this time they’re facing another predicament yet again! The three pigs brought a bunch of their pig friends into a tree, which is a connected undirected graph with $V$ vertices and $V-1$ edges. Originally there were...	30,126
The Fox and the Owl Description: Fox Mithra has finally learned the numbers and he is now familiar with the concept of ‘one’, ’two’, ‘three’ and also even ‘zero’, ‘minus one’, ‘minus two’ and so on. Really, an achievement for such a small fox. He took the textbook and copied the integers from the book ...	30,127
The Giant Description: You have been captured by an evil giant. You are both in a $N \times M$ big cave consisting of all points with integer coordinates $(x, y)$ such that $0 \le x < N, 0 \le y < M$. The giant plans to eat you, so you must escape before it’s too late! The giant is standing with his fe...	30,128
The Gourmet Description: The French gourmet Frank is a very well-respected gourmet; his job involves going around to various restaurants, eating their food and then writing a review about the restaurant. But he carries a dark secret: he is actually only interested in eating as much as possible and in a...	30,129
The Grand Adventure Description: We’d like to know if Jim will be able to complete his adventure before he even starts! ## Input The first line contains a single integer $n$, $1 \le n \le 5$, the number of adventures. Each of the next $n$ lines contains a single string $a$, a sequence of $\{ \$ ,...	30,130
The Great Egg Hunt Description: Every year at Easter Bob’s grandmother organizes The Great Egg Hunt in their family mansion. This has been a family tradition since even before Bob was born. Bob’s grandmother starts by filling up a giant Easter Egg with candy. She then picks a room (uniformly) at random and...	30,131
The Ice Cream Game Description: Kirderf and Slin are early to a great party where ice cream is served to everyone. Right now they are alone in the party hall where $N$ jars of ice cream are placed in a row on a table. There are $K$ different flavours of ice cream, where each flavour is represented by a...	30,132
The Ice Puzzle Description: Olle hates crosses. They remind him too much of getting a Wrong Answer verdict in Programmeringsolympiaden. When he arrived at Vallhamra Icehall and saw that there were $K$ ($2 \leq K \leq 20000$) crosses placed on the ice, he became angrier than a raging bull. Being th...	30,133
The Imp Description: You arrive in Ye Olde Magic Shoppe with some hard-earned gold to purchase wondrous and unique magic items. There are $n$ such items in the shop, each of them locked in a special magic box. The $i$-th box costs $c_ i$ gold pieces to buy, and contains an item worth $v_ i$...	30,134
The Key to Cryptography Description: Suppose you need to encrypt a top secret message like “SEND MORE MONKEYS”. You could use a simple substitution cipher, where each letter in the alphabet is replaced with a different letter. However, these ciphers are easily broken by using the fact that certain lett...	30,135
The King of the North Description: Winter is coming (or going? who can be sure these days) and a new king rises in the North. The message travels quickly these days... That is why you, the rising king, have not much time left. You need to rally your bannermen behind you. But one question seems harder t...	30,136
The King's Guards Description: In a certain kingdom, the king wants to protect his citizens by deploying guards. He has recruited a number of guards, and has outfitted them with heavy armor for protection from bandits, foreign knights, and other ne’er-do-wells. His guards are tough, but unfortunately t...	30,137
The King's Walk Description: Chess is a game in which two sides control pieces in an attempt to capture each other’s king. The pieces vary in mobility. At the beginning of a game the kings are rather vulnerable. They are less mobile than most other pieces and they tend to hide behind their pawns. Like ...	30,138
The Last Crusade Description: Scootaloo’s parents, Snap Shutter and Mane Allgood, have been away for many, many moons, venturing across the land in search of exotic flora and fauna for the advancement of Equestrian science and medicine. The gravity of their profession meant that they could never find t...	30,139
The Last Laugh Description: The self-proclaimed “super duper party pony” and amusement factory owner Cheese Sandwich has lost his laugh, and it’s up to his longtime pal Pinkie Pie to get it back. By now, Pinkie Pie has pulled out all the stops to get her “partier” in crime to laugh, all to no avail. As a ...	30,140
The Last Pizza Description: Penny and Pontus have bought $N$ pizzas and are currently eating. They are both polite Swedes, so no one wants to take the last slice. Penny can either take the rest of a pizza (provided it has at least one slice) or a slice from one of the pizzas. Then Pontus will do the sa...	30,141
The Last Problem Description: This is where the magic happens This is where magic lives Our friendships weave together stronger The bonds grow deeper, lasting longer And the greatest spell you’ll know Is how the Magic of Friendship grows... In the distant future, an older Twilight Sparkle is visited b...	30,142
The Leprechaun Hunt Description: In Irish mythology, a Leprechaun is a small sprite who stores all his treasure in a hidden pot of gold at the end of the rainbow. If someone is able to catch the Leprechaun, he must give that person his pot of gold. In this problem, we explore the difficulty of capturin...	30,143
The Magical 3 Description: Even more magically, almost all integers can be represented as a number that ends in 3 in some numeric base, sometimes in more than one way. Consider the number 11, which is represented as 13 in base 8 and 23 in base 4. For this problem, you will find the smallest base for a ...	30,144
The Mailbox Manufacturers Problem Description: In the good old days when Swedish children were still allowed to blow up their fingers with fire-crackers, gangs of excited kids would plague certain smaller cities during Easter time, with only one thing in mind: To blow things up. Small boxes were easy t...	30,145
The Maze Makers Description: The Maze Makers is a publisher of puzzle books. One of their most popular series is maze books. They have a program that generates rectangular two-dimensional mazes like the one shown in Figure 1. The rules for these mazes are: (1) A maze has exactly two exterior cell walls...	30,146
The N Days of Christmas Description: Consider the first three verses of the classic Christmas carol, The Twelve Days of Christmas: On the first day of Christmas my true love gave to me A partridge in a pear tree. On the second day of Christmas my true love gave to me Two turtle doves, And a par...	30,147
The Owl and the Fox Description: Fox Mithra has finally learned the numbers and he is now familiar with the concept of ‘one’, ’two’, ‘three’ and also even ‘zero’, ‘minus one’, ‘minus two’ and so on. Really, an achievement for such a small fox. He took the textbook and copied the integers from the book ...	30,148
The Paladin Description: A Paladin, a warrior adept at holy magic, needs your help forming spells. Being a Paladin, every spell must also be a Palindrome, meaning that it is the same string when read forwards and backwards. The cost of constructing a new spell is based on rune pair costs (costs of adja...	30,149
The Plank Description: You want to construct a long plank using smaller wooden pieces. There are three kinds of pieces of lengths $1$, $2$ and $3$ meters respectively, each which you have an unlimited number of. You can glue together several of the smaller pieces to create a longer plank. If the plank sho...	30,150
The Point of No Return Description: Twilight Sparkle forgot to return a book to the Canterlot Library, and it’s been two years—eight seasons—since she borrowed it! As a consequence, not only has she lost her perfect library book return record, she’s also had to pay a fine of twenty-eight bits; and, pos...	30,151
The Polar Express Description: It’s almost December, and the Polar Express is planning for its annual trip towards the North Pole. The Polar Express is a train with $N$ carts numbered $1$ to $N$, and you are the conductor! However, due to an exceptionally heavy snowstorm, your train recently ra...	30,152
The Power of Substitution Description: A substitution cipher uses a substitution table that for each letter $x$ in the alphabet assigns another (possibly the same) letter $p[x]$ in the same alphabet. A message $m_1\, m_2\, m_3\, m_4$ is then encrypted as $E_ p(m_1\, m_2\, m_3\, m_4)=p[m_1]\, p[...	30,153
The Princess and the Pea Description: A single pea is hidden in one of the $M$ mattresses at court. Your job is to find it within $N$ nights. Luckily, the kind princess has agreed to help you. After a single night’s sleep on a pile of mattresses, she can determine with certainty whether she slept on th...	30,154
The Punctilious Cruciverbalist Description: A crossword puzzle consists of a grid of squares in which intersecting words are placed, one letter per square. Some grid squares are filled black indicating that no letter should go there. Solvers are given clues for each word, and each clue is identified by...	30,155
The Queen's Super-circular Patio Description: The queen wishes to build a patio paved with of a circular center stone surrounded by circular rings of circular stones. All the stones in a ring will be the same size with the same number of stones in each ring. The stones in the innermost ring will be pla...	30,156
The Rectangles Are Surrounding Us! Description: You are given a list of rectangle boundaries. Each rectangle boundary is on integer coordinates. The rectangles surround squares on the coordinate grid. Your job is to determine the total number of such grid squares that are surrounded by at least one of ...	30,157
The Red Gem Description: The curator has decided to spice up the display, and has placed the gem on a purple circular platform, along with mundane orange circular gems. Starved citizens of circle land (points) have flocked to see the grand exhibit of the exquisite red gem. They cannot step on the purp...	30,158
The Safe Secret Description: One of the brightest and richest dukes of the nineteenth century built a break-in-proof room for storing his valuables and chose the lock secret code in an ingenious manner. He was so afraid of being robbed that he did not tell anyone the safe secret; he only wrote the way ...	30,159
The SetStack Computer Description: Given this importance of sets, being the basis of mathematics, a set of eccentric theorist set off to construct a supercomputer operating on sets instead of numbers. The initial SetStack Alpha is under construction, and they need you to simulate it in order to verify ...	30,160
The Silk Road ... with Robots! Description: Parts of the ancient silk road passed through southern Kazakhstan. You’ve been fantasizing about a modern silk road, which has its own special features. Along your fantasy road are robots as well as stores holding stashes of tenges (the national currency of...	30,161
The Sock Pile Description: This problem is based on an (almost) true story. A child, who shall remain nameless, has a large pile of clean socks. This pile contains $m$ pairs of socks with pictures and patterns and $n$ pure white socks. Each pair of socks consists of two identical socks and every pair i...	30,162
The Sound of Silence Description: In digital recording, sound is described by a sequence of numbers representing the air pressure, measured at a rapid rate with a fixed time interval between successive measurements. Each value in the sequence is called a sample. An important step in many voice-processing ...	30,163
The Stock Market Description: Evelina is going to start speculating on the stock market to become rich. She is actually not really interested in economics and never bothers to read more than the first stock price in the newspaper. But, she thinks, it’s everyone else who is complicating things. If you b...	30,164
The Summer Sun Setback Description: The Summer Sun Celebration is a major Equestria-wide festival that has been held every year since the defeat of Nightmare Moon at the hooves of Princess Celestia over a thousand years ago. It has been a long, long way since; one could hardly imagine today that any ...	30,165
The Triangle Factory Description: Tristian works at a triangle factory. His job is to classify different types of triangles produced in the factory. Tristian now asks you to write a program that can replace him. Tristian will give you three positive integers, $a$, $b$, and $c$. These are the three angles of a...	30,166
The Trip Description: A number of students are members of a club that travels annually to exotic locations. Their destinations in the past have included Indianapolis, Phoenix, Nashville, Philadelphia, San Jose, and Atlanta. This spring they are planning a trip to Eindhoven. The group agrees in advance...	30,167
The Trip, 2007 Description: A number of students are members of a club that travels annually to exotic locations. Their destinations in the past have included Indianapolis, Phoenix, Nashville, Philadelphia, San Jose, Atlanta, Eindhoven, Orlando, Vancouver, Honolulu, Beverly Hills, Prague, Shanghai, and...	30,168
The Uncertainty of Politics Description: * There are many committees, and thus many hearings, some of which take place at overlapping times. * While the committees are extremely punctual in terms of when to start a hearing, they are notoriously unpredictable in terms of how long the hearing ...	30,169
The Ups and Downs of Investing Description: Liam is heavily invested in the stock market, and has various theories that he uses to predict when the market will rise and when it will fall. Lately, things haven’t been going too well – the only thing rising is his frustration and the only thing falling is...	30,170
The Uxuhul Voting System Description: One of the world’s first civilisations was that of the ancient Uxuhul indians, in the jungles of Central America. The Uxuhul culture flourished for almost a thousand years, with its golden era around 3200 BC. Each year high priests, representing different parts of ...	30,171
The Weight Of Words Description: You are asked to write an AI that can play this game! ## Input The input consists of a single line with two integers $l$ ($0 < l \le 40$) and $w$ ($0 < w \le 1000$). ## Output Output a string of length $l$ with weight $w$ consisting of lowercase English letters if it ex...	30,172
The White Rabbit Pocket Watch Description: Alice: How can it be? Rabbit: Trust me Alice. It always takes the same time. When I go from my home up the road to Queen of Hearts’ Castle, my watch counts nine hours. However, if I continue down to Mad Hatter’s House, my watch counts just two hours in total. ...	30,173
The Wire Ghost Description: Žofka is bending a copper wire. She starts with a straight wire placed on the table with the starting point glued to the middle of the table. She then repeatedly picks a point on the wire and bends the part starting at that point (away from the starting point) by $90$ de...	30,174
The Wizard Theodor Description: A small army of $N$ monsters is just outside Tästerås! Now it is up to the wizard Theodor to defeat them and save the city. Each monster has a certain amount of life points. To damage the monsters, Theodor can fire magical explosions. Each time he fires an explosion, ...	30,175
The Worm in the Apple Description: Willy the Worm was living happily in an apple – until some vile human picked the apple, and started to eat it! Now, Willy must escape! Given a description of the apple (defined as a convex shape in 3D space), and a list of possible positions in the apple for Willy (d...	30,176
The Wrath of Kahn Description: Topologically sorting the nodes of a directed graph (digraph) $G$ means putting the nodes in linear order such that whenever there is an edge from node $x$ to node $y$ in $G$, $x$ always precedes $y$ in the linear ordering. It is not hard to show that the nodes of a digraph ...	30,177
Theme Park Description: Roller coasters are so much fun! It seems like everybody who visits the theme park wants to ride the roller coaster. Some people go alone; other people go in groups, and don’t want to board the roller coaster unless they can all go together. And everyone who rides the roller coa...	30,178
Theodor the Wizard Description: This problem is based on the problem The Wizard Theodor. Evil Olle, who is ultimately responsible for all evil, is tired of Theodor always ruining everything. Now, Olle has devised a new malicious plan, and to put it into action, he needs to keep Theodor occupied. At hi...	30,179
Thermostat Trouble Description: Earth has recently been visited by aliens, and is now a member of a galactic federation consisting of many other advanced lifeforms on numerous habitable planets. This federation is very impressive in its scope and accomplishments, but unfortunately the usual failures of...	30,180
Thesaurus Description: After staying up all night, Yraglac has finally finished writing the essay for his assignment. However, he just noticed at the last minute that his essay exceeds the maximum permissible length! Since Yraglac has little time left, he doesn’t want to spend too much time changing h...	30,181
Thieving Residents Description: Bergurby has $N+1$ buildings (houses + City center) which are connected by $N$ roads. Each building connects to at most $3$ roads, and it is possible to travel from any building to another. There are $N$ people numbered $1, 2, ..., N$ and they each live in a ...	30,182
Thin Ice Description: Uolevi is at a frozen lake in the shape of an $n \times m grid$, with one coin on each square. Each square has a durability: the maximum number of coins the ice on the square can withstand. In one step, Uolevi can move one square up, down, left or right, but not outside the lake. If ...	30,183
This Ain't Your Grandpa's Checkerboard Description: You are given an $n$-by-$n$ grid where each square is colored either black or white. A grid is correct if all of the following conditions are satisfied: * Every row has the same number of black squares as it has white squares. * Every column has the...	30,184
Thore's self-esteem Description: ## Input The first line of the input contains a single number $n$, where $1 < n \leq 100$. Then follows $n$ lines with a name on each line. Each name only contains characters from the set $\big [\text {a-zA-Z}\big ]$, i.e. lower and upper case English letters. Each name ...	30,185
Thoring test Description: Thore loves chatting with an AI chatbot. It will tell him that he is handsome, intelligent and that he sings like an angel, all the things he wants to hear. And it is never rude or makes spelling errors like those pesky humans. Now Thore wants your help to write a program that...	30,186
Three Dice Description: Given a list of three-letter words, generate one possible set of three, six-sided dice such that each word can be formed by the top faces of some arrangement of the three dice. You must distribute 18 distinct letters across the 18 total faces of the dice. There may be multiple p...	30,187
Three Digits Description: Per is obsessed with factorials. He likes to calculate them, estimate them, read about them, draw them, dream about them and fight about them. He even has the value of $12!=479\, 001\, 600$ tattooed on his back. He noticed a long time ago that factorials have many trailing ze...	30,188
Three Kinds of Dice Description: To formalize this: define a “die” as any shape with at least one face such that each face shows a positive integer. When a die is rolled, one of its faces is selected uniformly at random. When two dice roll against each other, the die whose selected face shows a higher ...	30,189
Three Powers Description: Consider the set of all non-negative integer powers of 3. * $S = \{ 1, 3, 9, 27, 81, \ldots \} $ $S = \{ 1, 3, 9, 27, 81, \ldots \} $ Consider the sequence of all subsets of $S$ ordered by the value of the sum of their elements. The question is simple: find the set ...	30,190
Three in a Row Description: The mathematician Lenore Oljer has done so much math that she has grown tired of prime numbers. She has now started studying so-called “nice triplets”. It’s very easy to create a nice triplet. Start with an integer $a$ greater than zero and then create the triplet $(a, a+1, ...	30,191
Three-State Memory Description: For example, $201$ in this strange representation is $2\cdot 2^2+0\cdot 2^1+ 1\cdot 2^0=9$. Some numbers are shorter in this representation, but for other numbers it doesn’t help at all – for instance, $15$ is $1111$ in binary and this is the only way of writing it in th...	30,192
Threes and Fives Description: You are given a positive integer $n$ and should print the sum of positive integers $< n$ which are a multiple of either $3$ or $5$. ## Input The first and only line of input contains a positive integer $n \leq 10^{18}$. ## Output Print the sum of positive integers $< n$ wh...	30,193
Through the Grapevine Description: According to Wikipedia, to hear something “through the grapevine” is to learn of something informally and unofficially by means of gossip or rumor. In this problem, you are tasked with determining how many people will hear about a particular rumor “through the grapevi...	30,194
Throwing bridges Description: In the province of Wulingyuan in China, there are $N$ very steep cliffs. It is very popular for tourists to visit the mountain peaks. Often, they even want to visit more than one in order to take photos from different angles. To facilitate this, several suspension bridges...	30,195
Thwack! Description: The game Thwack is played on a 1-dimensional grid of cells: the game board. Each grid cell contains either a black stone, a white stone, or is empty. Two players alternate taking turns. A turn consists of choosing two adjacent stones of opposite colours and then choosing one of th...	30,196
Tic Tac Toe Description: The game of Tic Tac Toe is played on an $n$-by-$n$ grid (where $n$ is usually but not necessarily three). Two players alternate placing symbols on squares of the grid. One player places Xes and the other player places Os. The player placing Xes always goes first. When the grid cont...	30,197
Tic Tac Toe Description: Tic Tac Toe is a child’s game played on a $3$ by $3$ grid. One player, X, starts by placing an X at an unoccupied grid position. Then the other player, O, places an O at an unoccupied grid position. Play alternates between X and O until the grid is filled or one player’s symbol...	30,198
Tic Tac Toe Counting Description: Tic Tac Toe is a simple children’s game. It is played on a $3 \times 3$ grid. The first player places an X in any of the $9$ cells. The next player places an O in any of the remaining 8 cells. The players continue to alternate placing Xs and Os in unoccupie...	30,199

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