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Bribing Eve Description: Eve works at a magazine that does product reviews and publishes recommendations to consumers. They are working on a new mobile phones review and have decided on two reproducible tests that score each device’s battery lifetime and performance using an integer between $1$ and $10...
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Brick Wall Description: Pat and Mat are trying to build a brick wall. They have three types of bricks—all have the same depth and height but they are of three different widths: 1, 2, and 3. As every builder knows (and Pat and Mat learned after watching their walls fall down quite a few times), a wall i...
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Bricks Description: You are given a sequence of white (W) and black (B) bricks. The goal is to partition it into some number of non-empty, contiguous blocks, each one having the same ratio of white and black bricks. Of course one can always “partition” the sequence into one single block (which is not ...
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Bricks Description: Josefine is playing a tetris-like game called bricks. The game takes place in a rectangular grid with $6$ columns $\times \; 8$ rows. A brick takes up a $1 \times 1$ slot in the grid. Initially the grid is empty. A brick formation is a rectangle where some parts are filled with bric...
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Brickwork Description: Bob the Builder is tired of building tiny houses and paving narrow roads, and he strives for something bigger. The new job given to him by a very eccentric client is exactly what he needs: He is tasked with building a wall of a certain width that is infinitely high! His client as...
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Bridge Description: $n$ people wish to cross a bridge at night. A group of at most two people may cross at any time, and each group must have a flashlight. Only one flashlight is available among the n people, so some sort of shuttle arrangement must be arranged in order to return the flashlight so ...
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Bridge Automation Description: In Delft there are a number of bridges that are still being operated by a human, known as the bridge operator. One such bridge operator will soon retire, hence there is the need for a replacement. The Bridge And Poker Committee has decided to use a computer program to aut...
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Bridge Builders Description: The king wants bridges built and he wants them built as quickly as possible. The king owns an $N \times M$ grid of land with each cell separated from its adjacent cells by a river running between them and he wants you to figure out how many man-hours of work it will take to...
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Bridge building Description: In ancient days, long before even LTH existed, there were $M$ pairs of lovers living along the Söderåsen ridge. Each of the $2M$ people lived at some integer distance in meters from the start of the ridge, and unfortunately, not in the same place as their partner. The shap...
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Bridges and Tunnels Description: Some days, the university campus gets very wet. Other days, it can get very cold. Although many times, it is pleasant to be outside, there are days when we would prefer to stay indoors. Luckily, the campus designers have gradually connected the various buildings with t...
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Bridges and Tunnels 2 Description: It may feel warm now, but in a few months, Waterloo will be full of snow. Luckily, many of the buildings on campus are connected by bridges and tunnels, so you do not need to go outside very much. The network of buildings can be confusing, and it is hard to know the b...
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Bridging Signals Description: “Oh no, they’ve done it again”, cries the chief designer at the Waferland chip factory. Once more the routing designers have screwed up completely, making the signals on the chip connecting the ports of two functional blocks cross each other all over the place. At this lat...
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Bridging the Gap Description: For example, Sample Input 1 assumes the bridge can hold $2$ walkers at a time and there are $4$ walkers with crossing times $1$ minute, $2$ minutes, $5$ minutes and $10$ minutes, respectively. The shortest time of $17$ minutes can be achieved by the following seque...
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British Menu Description: Since you are in Britain, you definitely want to try British food. Unfortunately you will only have a single free evening, so you decided to try all the food you can get in one run. You plan a gigantic meal where you eat one British dish after the other. Clearly not every orde...
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Brocard Point of a Triangle Description: The Brocard point of a triangle $ABC$ is a point $P$ in the triangle chosen so that: $\angle PAB = \angle PBC = \angle PCA$ (see figure below). The common angle is called the Brocard angle. The largest Brocard angle is $\pi /6$ which is the Brocard angle for ...
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Broken Calculator Description: Working on math homework late one night, you realized your calculator is broken. When it performs “addition” it adds the two numbers entered, then subtracts the result from the previous operation. When it performs “subtraction” it subtracts the two numbers entered, then m...
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Broken Calculator Description: You have a calculator, but unfortunately, it is broken. The (broken) calculator can maintain a variable $v$, which is initially $0$. There are only three things that it can do correctly (and, even then, it takes quite a bit of time): * You can increment $v$; in other words, ...
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Broken Keypad Description: Astronauts are trained for all kinds of contingencies before launch day, and have a unique identifier number for every problem they could possibly come up with. As soon as they identify the problem, they plug the identifier into a keypad to send the information to their crew-...
26,617
Broken Minimum Spanning Tree Description: Ethan was tasked with finding a minimum spanning tree of a weighted, connected, undirected graph. However, he misunderstood the task and found a spanning tree that may not be minimal. To make his spanning tree a minimum spanning tree, you perform a sequence of ...
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Broken Swords Description: Ken is a fencer with a big problem: he swings too hard! Whenever Ken gets a new sword, he’s sure to break it sooner rather than later. It’s occurred to him that this habit is costing him quite a bit of money, since he normally buys a new sword whenever his current sword breaks. ...
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Brownian Bears Description: Dr. Ursula Major is an internationally renowned expert in the study of bears, specifically brown bears, which are known in many parts of North America as grizzly bears. She is most famous for her discovery of an extremely rare brown bear subspecies — the Brownian bear, whose...
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Brownie Points I Description: Stan and Ollie play the game of Odd Brownie Points. Some brownie points are located in the plane, at integer coordinates. Stan plays first and places a vertical line in the plane. The line must go through a brownie point and may cross many (with the same $x$-coordinate). T...
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Brownie Points II Description: Those lines divide the plane into four quadrants. The quadrant containing points with arbitrarily large positive coordinates is the top-right quadrant. The players score according to the number of brownie points in the quadrants. If a brownie point is crossed by a line, it ...
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Brunhilda's Birthday Description: Except for her affinity towards old armours, Brunhilda is a normal seven year old girl. Thus, she is planning the perfect birthday party, for which she has invented the following game: All children run around until some number $k$ is announced. Then all children try to...
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Brýr Description: As everyone knows from last year, Eva and Stefán live in Vestmannaeyjar. You helped Eva find the best travel plan to tour the entire country with Stefán in the least amount of time. Now Eva wants to visit Egilsstaðir, but travelling around the country lead to them finding out that Ste...
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Bubbly Troubly Description: You may have seen a champagne tower at a wedding or an exclusive Hollywood A-list party. In a typical three-level tower, the first (lowest) level contains $9$ glasses touching in a square pattern. The second level contains $4$ glasses touching in a square pattern centered ab...
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Bucket Brigade Description: You are at one end of a line of $n$ people. You and the other $n-1$ people are holding one bucket each, each with a capacity of $x$ liters. You want to move a total of $v$ liters of water from a large tub next to you to a similar tub at the other end of the line. You use...
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Budget Description: I have a problem. I was supposed to make a budget proposal for this competition and I haven’t started yet. It must be done at the end of the competition or the others will notice that I haven’t done it. This is where I need you. The budget proposal is a matrix where the rows represent ...
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Buenos Airlines Description: Alice and Bob dream about future summer vacations where travel is unconstrained by pandemics, budgetary constraints, or other mundane problems. Since they love winter, they want to visit the Southern Hemisphere, in particular Chile. Chile is, geographically speaking, a rath...
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Buffed Buffet Description: You are buying lunch at a buffet. A number of different dishes are available, and you can mix and match them to your heart’s desire. Some of the dishes, such as dumplings and roasted potatoes, consist of pieces of roughly equal size, and you can pick an integral number of suc...
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Buggy Robot Description: Your friend just bought a new programmable robot and has asked for your help. The robot operates in a 2D grid that may contain obstacles. The environment has a known start location and a known goal location. The robot is controlled with a string consisting of commands L, R,...
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Buggy Robot Description: There is a robot in a 2D grid. The grid consists of empty cells and obstacles, and there is exactly one cell that is the exit. The robot will exit the grid if it ever reaches the exit cell. Empty cells are denoted as ‘.’, the robot’s initial position is denoted as ‘R’, obstacle...
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Build Dependencies Description: ## Input The input consists of: * one line with one integer $n$ ($1\leq n \leq 100\, 000$), the number of Makefile rules; * $n$ lines, each with a Makefile rule. Such a rule starts with “$f$:” where $f$ is a filename, and is then followed by a list of ...
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Build a Boat Description: An oft-forgotten part of a well-rounded software engineer’s training is those long but vital months spent learning the art of shipwrighting. Modern boats, as we know, are superbly safe, to the point that they are nigh unsinkable. Even in a head-on collision the ship can be sa...
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Building Boundaries Description: Maarja wants to buy a rectangular piece of land and then construct three buildings on that land. The boundaries of the buildings on the ground must have rectangular sizes $a_1 \times b_1$, $a_2 \times b_2$, and $a_3 \times b_3$. They can touch each other but they m...
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Building Fences Description: Donald is a fence builder. He wants to build a fence that is $N - 1$ meters long. He needs a fence post every meter along the fence, which means he needs $N$ fence posts. Donald has $K$ poles of varying lengths that he wants to use as fence posts. The fence posts mu...
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Building Highways Description: The country of Singanesia consists of $N$ cities, numbered from $1$ to $N$. From a recent survey, each city is assigned a level which denote how problematic it is. The $i$-th city have a problematic level of $A_ i$. To improve the welfare, recently there is a plan to ...
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Building Pyramids Description: When initiating a larger project, like building a pyramid, it’s best to think twice. Your task today is to write a program that computes how high a pyramid can be built given a certain number of blocks of stone. We assume that the pyramid to be built is compact, i.e. the...
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Building Roads Description: A multi-billionaire has a vision to build a completely new city from scratch. After much research and consultations, locations have been selected for all the houses, shopping malls, restaurants, etc. Roads now have to be added to ensure that every location is reachable by an...
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Built to Scale Description: A factory is making widgets of weights up to $N$ using $K$ types of metal pieces with different weights. There are unlimited copies of each type of metal piece. Every widget must have a certain weight; any of the metal pieces can be used to construct each widget, as long as ...
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Buka Description: Quite often there is substantial noise in the classroom during class. Instead of paying attention to what the teacher is saying, the students rather discuss the economic crisis or Croatia’s joining the European Union. The biggest noise often occurs when the students are idle, so teac...
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Bulldozer Description: You are tasked with bulldozing some buildings that stand along a long, straight road. The buildings are modelled as evenly spaced stacks of identical square blocks along an infinite line. Your powerful bulldozer is capable of moving any one of these blocks one unit of distance to...
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Bumped! Description: Peter returned from the recently held ACM ICPC World Finals only to find that his return flight was overbooked and he was bumped from the flight! Well, at least he wasn’t beat up by the airline and he’s received a voucher for one free flight between any two destinations he wishes. ...
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Bumper-To-Bumper Traffic Description: The road is modelled as the real line (units in meters). So a car is identified with its position on the line. Also, cars are $4.4$ meters long. Given initial positions of two cars that are driving along the real line in the positive direction and a transcript of ...
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Bundles of Joy Description: For example, you can buy the “Chocolate Cakes” bundle which includes chocolate layer cake and black forest cake for $20. Or you can buy the “Fruity Cakes” bundle which includes lemon pound cake and key lime cake, also for $20. They offer an even bigger bundle that includes a...
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Bungee Builder Description: A new bungee jumping attraction is to be built at a mountain range of $N$ mountains of heights $H_1, H_2, \ldots , H_ N$. This project involves constructing a horizontal bridge connecting two distinct mountains, on which the attraction will be opened. The bridge may be b...
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Bungee Jumping Description: Once again, James Bond is fleeing from some evil people who want to see him dead. Fortunately, he has left a bungee rope on a nearby highway bridge which he can use to escape from his enemies. His plan is to attach one end of the rope to the bridge, the other end of the rope...
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Bunny Town Bonding Description: As long as anyone can remember, Bunny Town has been home to many happy and friendly bunnies living together peacefully. However, a recent misunderstanding has led to serious disputes and relationship issues. Now most of the bunnies have stopped talking to each other, and...
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Burglary Description: The giant Candy-Bar Wall in the Royal Kitchen is used to store…well, candy bars. These are placed in jars on $N$ equal-length shelves. The shelves are positioned in a vertical progression from the ground up, and perfectly aligned horizontally on their rightmost and leftmost ed...
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Buried Treasure Description: You may be under the impression that treasure maps originate from pirates, who create maps after burying their treasure so that they will later have a way to retrieve their stolen fortunes. In reality, it is extremely rare for pirates to bury treasure; there are only a few ...
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Buried Treasure Description: Buried treasure can be found using treasure maps. There are $m$ different locations numbered from $1$ to $m$. Each location contains either treasure or a trap. Joey gives you $n$ treasure maps. Each treasure map has two markers $m_1, m_2$. For $i\in \{ 1,2\} $, if $m_ ...
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Burizon Fort Description: On Mars there is a huge complex of forts. Martians living in these forts are fond of eating Burizons and get very grumpy if they run out of them. Therefore it’s quite common task to transport Burizons among these forts when the supplies are running low somewhere. The transpor...
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Burrows-Wheeler Description: The Burrows-Wheeler transform is a technique for transforming a text message so that it responds well to compression techniques. Under this transform, we consider all cyclic shifts of an input string. For example, if our text was the string “arbitrary string”, then the stri...
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Bus Description: A bus with $n$ passengers opens its door at the bus stop. Exactly half of its passengers and an additional half of a passenger get out. On the next stop, again, half of the passengers plus half of a passenger leave the bus. This goes on for $k$ stops in total. Knowing that the bus ...
26,653
Bus Assignment Description: The Institution for Carrying People Carefully is responsible for managing the famous Line Bus in Line Town. The Line Bus goes through $n$ stops conveniently numbered from $1$ to $n$. At stop $i$, $a_i$ people first get off the bus. Then, $b_i$ people get on the bus. The ...
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Bus Clock Display Description: When you travel to Egypt, you will probably want to enjoy the famous pyramids and possibly also to take a bus to Luxor to visit the Valley of the Kings. To overcome boredom during such a long trip, imagine you are trying to keep yourself occupied by observing a large cloc...
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Bus Lines Description: After many years without any public transport, the town Krockholm will finally get a network of bus lines. The plans are still on the drawing board, but it has been decided that there shall be $n$ stations labelled $1$ to $n$, and $m$ bus lines where each line connects tw...
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Bus Numbers Description: Your favourite public transport company LS (we cannot use their real name here, so we permuted the letters) wants to change signs on all bus stops. Some bus stops have quite a few buses that stop there and listing all the buses takes space. However, if for example buses $141$, ...
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Bus Numbers Description: It is from this story the taxicab numbers got their name. The $n$’th taxicab numbers is defined to be the smallest number that can be expressed as a sum of two positive cube numbers in $n$ distinct ways. It turns out that these numbers grows rather quickly. This makes them...
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Bus Planning Description: You are to write a program which helps her with the task of making these groups. Given the number of kids and their enemies, find the minimum number of groups required, as well as a division of the class into this minimum number of groups ## Input The first line contains three i...
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Bus Schedules Description: Imagine that you happen to be the one to advance to the World Finals. Sounds good, doesn’t it? Then you would be going to travel by various means of transport: airplanes, trains, buses, etc. Are you ready for that? This problem tries to evaluate your orientation skills in bus...
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Bus Ticket Description: Dang it! Your period ticket for the local Bus-Go-On-system (BGO) has expired. At first you wanted to buy a new period already today, but you suddenly realize that your next ticket would then expire a few days before your vacation starts, leaving a few trips you need to pay for i...
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Bus Tour Description: Imagine you are a tourist in Warsaw and have booked a bus tour to see some amazing attraction just outside of town. The bus first drives around town for a while (a long while, since Warsaw is a big city) picking up people at their respective hotels. It then proceeds to the amazing...
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Busy Board Description: Remember the busy boards for toddlers that have an array of holes into which to hammer pegs of various shapes? There’s a new, electronic version. The board consists of a 2D grid of pegs. Each peg on the board can be either up or down, but not both simultaneously. You can pick an...
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Busy Roads Description: Robert lives in ERPLand, a country with $N$ cities numbered 1 to $N$. Each day in this country has $C$ seconds, numbered 0 to $C - 1$. There are $M$ bi-directional roads connecting pairs of cities. Road $i$ connects cities $A_ i, B_ i$, takes Robert $T_ i$ seconds to travel ...
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Busy Schedule Description: You have a busy schedule to keep up with. Every time you make a new appointment, you scribble the starting time down on a little note pad. At the start of every day (12:00 a.m.), you sort the appointments for that day from earliest to latest and then go to sleep. Instead of h...
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Button Bashing Description: You recently acquired a new microwave, and noticed that it provides a large number of buttons to be able to quickly specify the time that the microwave should be running for. There are buttons both for adding time, and for subtracting time. You wonder how efficient you can b...
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Buying Books Description: You are going to buy $N$ books of different kinds (numbered from $1$ to $N$), and are currently checking the different Internet book stores for prices. Each book is sold by at least one book store, and can vary in prices between the different stores. Furthermore, each book sto...
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Buying Coke Description: I often buy Coca-Cola from the vending machine at work. Usually I buy several cokes at once, since my working mates also likes coke. A coke in the vending machine costs $8$ Swedish crowns, and the machine accept crowns with the values $1$, $5$ and $10$. As soon as I press the c...
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Buying Fika Description: Ever since little Kalle won a free car wash from a scratch-off ticket, he has started to see life differently. He has begun to notice that he has an immense amount of luck in everyday situations. A fraction of the extraordinary events he has recently experienced includes winnin...
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Buzzwords Description: The word the is the most common three-letter word. It even shows up inside other words, such as “other” and “mathematics”. Sometimes it hides, split between two words, such as “not here”. Have you ever wondered what the most common words of lengths other than three are? Your tas...
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Bílskúrar Description: Hannes lives in Brúnaland. In Brúnaland there is only one road and all the houses are on one side of the road. On the other side of the road there are garages, one for each house. The houses are numbered and the garage corresponding to house $i$ is also numbered $i$. It woul...
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Bíóferð Description: For example, if the seats are numbered from right to left then Sara doesn’t want to sit in the first seat. You get information about the preference of the group, who is going and where each person wants to seat. Can you help the group determine a satisfactory seating arrangement? ## ...
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Bíókort Description: Many years ago the Bíótríó was founded. The original members were Arnar, Hannes and Sara. The goal of the group was simple: Go to the cinema frequently and cheaply. They managed to go upwards of a hundred times per year, sometimes even more often. A few years after the founding Hal...
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CD Description: Jack and Jill have decided to sell some of their Compact Discs, while they still have some value. They have decided to sell one of each of the CD titles that they both own. How many CDs can Jack and Jill sell? Neither Jack nor Jill owns more than one copy of each CD. ## Input The inp...
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CDVII Description: Roman roads are famous for their longevity and sound engineering. Unfortunately, sound engineering does not come cheap, and a number of neo-Caesars have decided to recover the costs through automated tolling. A particular toll highway, the CDVII, has a fare structure that works as f...
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CHACTL Description: Seasoned competitive programmers are quite familiar with KACTL, a very good algorithm repository designed for use in the ICPC. The problem setters of Chalmers Challenge 2021 count themselves to this group, but have in preparation for this contest noticed two serious flaws with ...
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CPR Number Description: Danish citizens have a unique personal identification number in the Danish Central Person Register, called the CPR number. Each CPR number consists of ten digits. The first six digits represent the person’s day of birth. The following four digits are a sequence number. Until $...
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Caber Scoring Description: In the Highland Games Heavy Events, athletes compete over multiple throwing events and are scored based on their placement in each one. Most of the implements used in the competition have a regulated weight and size, except for the caber, which is used in the caber toss. The ...
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Cable Car Description: At $3\, 147.3$ meters high, Fansipan is the tallest mountain in the Indochina peninsula. To promote tourism, $n$ stations were built on the mountain, numbered from $1$ to $n$. Two companies, Mobi and Vina are in charge of operating cable cars connecting the stations. Each of the...
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Cactus Description: In a strongly connected directed graph, there is for every pair $u,v$ of vertices some directed cycle (not necessarily simple) that visits both $u$ and $v$. A directed graph is a cactus if and only if it is strongly connected and each edge is part of exactly one directed si...
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Cafeteria Description: Theta likes to play Lure of the Labyrinth, which is an online game that uses a compelling graphic novel storyline to engage middle grades students in mathematical thinking and problem-solving. To find lost pets, students have to infiltrate a world of monsters and solve puzzles! I...
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Cafeteria (Easy) Description: Theta likes to play Lure of the Labyrinth, which is an online game that uses a compelling graphic novel storyline to engage middle grades students in mathematical thinking and problem-solving. To find lost pets, students have to infiltrate a world of monsters and solve puz...
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Cairo Corridor Description: The Cairo pentagonal tiling is a decomposition of the plane using semiregular pentagons. Its name is given because several streets in Cairo are paved using variations of this design. Consider a bounded tiling where each pentagon is either clear (white) or filled in (grey). ...
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Cake Description: Žofka really likes cakes. Her most recent favorite is a rectangular-shaped cake with hard chocolate glazing and white marzipan roses on top. The glazing has been pre-cut in a grid-like pattern at the bakery since this type of glazing is difficult to cut after it hardens. The bakers pr...
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Cake Cutting Description: It’s SoCCat’s birthday, and they have baked a delicious cake for the occasion. Unfortunately, there are too many students in SoC who is attending the party and interested in eating the cake. It is not feasible to cut the cake into sectors, otherwise the angle of each sector wo...
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Cakey McCakeFace Description: Cakey McCakeFace’s signature pastry, the Unknowable Cake, is baked daily in their Paris facility. The make-or-break trick for this cake is the cooking time, which is a very well-kept secret. Eve, the well-known spy, wants to steal this secret, and your job is to help her. ...
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Calculating Dart Scores Description: Given a target score, output at most three throw scores such that their sum is equal to the given target score. Note that the centre of the dartboard, which is usually called bullseye, is not taken into account is this problem. ## Input The input consists of a single ...
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Calculator Description: ## Input Input contains several test cases, one per line. Each test case consists of an expression to be evaluated, containing numbers, parentheses, and the operators $+,-,*,/$. Normal operator precedence applies, so multiplication and division bind harder than addition and subtra...
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Call a Cab Description: Tourists in the numerous Welsh valleys are in need of an IT solution to their transportation troubles. They want to see all the local Points of interest (POIs) in a specific order already set out by their trusty tour guides. Visitors have to rely on various types of transportation:...
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Call for Problems Description: The Call for Problems for the ICPC North America Qualifier (NAQ) has finished, and a number of problems were proposed. The judges voted on the difficulty of each problem. The NAQ does not want to be considered an odd contest, so therefore they refuse to use any problem wh...
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Calories From Fat Description: Others recommend radically different amounts of fat. Dean Ornish, for example, suggests that less than 10% of total caloric intake should be fat. On the other hand, Robert Atkins recommends the elimination of all carbohydrate with no restriction on fat. It has been estima...
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Camp Lunches Description: You are a camp counselor at a summer camp and it is time to take some of the kids to lunch. There are $n$ groups of friends of different sizes who would like to be able to eat lunch together. There are $k$ bins that each hold exactly $x$ lunches. If one of the lunches in a...
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Can Tho Expressway Description: The governor of Can Tho is planning to build a new expressway in this city. The expressway will connect Can Tho and Ho Chi Minh City, bringing prosperity to the region. Naturally, the expressway cannot intersect with Can Tho’s famous tourist destination, ‘Cai Rang Floating ...
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Can of Worms Description: There is an old adage about opening a can of worms. A lesser known adage is one about shooting a can of exploding worms with a BB gun. Imagine we place some cans of exploding worms on a long, straight fence. When a can is shot, all of the worms inside will explode. Different ...
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Can't Stop Playing Description: Some computer games are extremely fun and this problem may be about one of these. You are given a sequence of one-dimensional blocks, each of length that is a power of two. The goal of the game is to merge all the blocks into one big block. The blocks are presented one ...
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Canadians, eh? Description: You have received a warning that foreign spies may have infiltrated the great country of Canada. Fortunately, you have developed a foolproof method to determine which potential suspects are truly Canadian: A person is a true Canadian if and only if they end every sentence ex...
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Candle Box Description: Rita loves her Birthday parties. She is really happy when blowing the candles at the Happy Birthday’s clap melody. Every year since the age of four she adds her birthday candles (one for every year of age) to a candle box. Her younger daydreaming brother Theo started doing the s...
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Candy Description: It is Saturday and Ann Britt-Caroline is going to buy candy. She has identified several different bags of candy she is considering buying. Each bag contains a number of pieces of candy of different types. There are $10$ types of normal candy (these are numbered $1, \ldots , 10$), an...
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Candy Description: In the ancient city of Ica, there is said to be a palace with wealth beyond imagination. Inside, there is a corridor with $N$ boxes of candy from all over the world. Travellers passing by can take as much candy as they want, provided that they pay its weight in gold. The boxes o...
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