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Fibonacci Cycles Description: Yraglac loves number sequences. One of his favourites is the classic Fibonacci numbers. He likes to set the base case as $F_0 = F_1 = 1$ and $F_ n = F_{n-1} + F_{n-2}$. Now, one can only list out the same numbers so many times before getting bored, so Yraglac came up ...
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Fibonacci Gjöf Description: Siggi got an array of $n$ positive integers, $x_1, x_2, \ldots , x_ n$ as a birthday gift from his grandmother. These integers aren’t just any integers, they denote Fibonacci numbers. The first Fibonacci number is $1$, the second Fibonacci number is also $1$ and the ones aft...
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Fibonacci Tour Description: Charles is traveling to the fantastic Fibonacci City. The city has $n$ mansions of various heights and $m$ bi-directional roads connecting the mansions. One of the most exciting tourist attraction in the city is the Fibonacci Tour, which is a simple path visiting a seque...
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Fibonacci Words Description: The Fibonacci word sequence of bit strings is defined as: Here $+$ denotes concatenation of strings. The first few elements are: $n$ $F(n)$ 0 0 1 1 2 10 3 101 4 10110 5 10110101 6 1011010110110 7 101101011011010110101 8 1011010110110101101011011010110110 9 10...
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Fibs og Dibs Description: In each round Dagur start by calling “Fibs”, when he does that they add their two numbers together and Dagur takes the new number, so that $a$ takes the value of $a + b$. Then Elvar says “Dibs” and they repeat the steps, except now Elvar takes the new number, so that $b$ t...
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Field Trip Description: You and your classmates are going on an exciting field trip to a downtown museum. Because the museum is an hour away, three buses of identical capacity and a van are dispatched as a means of transportation to the museum and back. The buses will first start loading only students,...
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Fifty Shades of Pink Description: ## Input Input starts with an integer $1 \leq N \leq 1\, 000$, the number of button packages in the box. The following $N$ lines each has a color name, one for each package. The names consist of up to 30 characters of letters A - Z, a - z. ## Output Print one integer, t...
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Fight to Survive Description: You are the head of a group of survivors in the zombie apocalypse. Just recently you’ve heard word of an incoming zombie horde heading to your facility. As commander in chief the responsibility falls on to you to prepare for the incoming invasion. Luckily these zombies a...
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Figurine Figures Description: The Miniature Toy Association (or MTA for short) is releasing the latest edition of its brand of collectible figurines. MTA used to sell them individually, but now has decided to adopt a new business strategy that involves randomly choosing $4$ figurines from the entir...
27,608
Fika Optimization Description: The yearly programming contest LTH challenge is coming up, and as contest organizer you of course want the contestants (especially those from Lund) to perform as well as possible. There are $M$ contestants competing from $N$ rooms. As contest organizer you know which...
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Filip Description: Mirko has a younger brother, Filip, who just started going to school and is having trouble with numbers. To help him get the hang of the number scale, his teacher writes two three-digit numbers. She asks Filip to compare those numbers, but instead of interpreting them with the leftmo...
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Filling Crates Description: Ada the Alewife wants to ship $n$ beers from her brewery, all neatly packed into as few crates as possible. Crates come in many different sizes: For integers $a, b$ with $a\geq 2$ and $b\geq 2$, a single crate of size $a\times b$ holds exactly $a\cdot b$ beers. N...
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Film Critics Description: There are $n$ critics numbered from $1$ to $n$ scheduled to watch the movie early, and each of them will watch it separately. After watching it, they will immediately give it a score from $0$ to $m$. Susan, the cinema owner, has carefully looked at every critic’s socia...
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Fimmtudagstilboð Description: Hafliði has been a regular at Mahjong Pizza’s Thursday-offer since its debut in 1993. The offer consists of a single pizza with two toppings for $1\, 000$ ISK, that is until January 2021 when it increased by $100$ ISK and has done so every year since. Hafliði wants you...
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Final Exam Description: In the final round of the Hunter Exam, candidates must prove their ability to process big data as well as geometry knowledge. In the Examination Hall, the candidates can find three piles of segments: * The first pile has $n_ a$ segments, and the $i$-th segment has length ...
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Final Exam Description: The Vietnamese High School graduation exam is in progress! For most Vietnamese high school students, this is their most important exam, as its result not only decides whether they can graduate from high school, but is also used for their university applications. Today, Hanh fin...
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Financial Planning Description: Being a responsible young adult, you have decided to start planning for retirement. Doing some back-of-the-envelope calculations, you figured out you need at least $M$ euros to retire comfortably. You are currently broke, but fortunately a generous gazillionaire friend has ...
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Find Poly Description: Consider a set of line segments in a 2D plane. For any set of line segments $L$, define $P(L)$ as the set of all endpoints of the line segments in $L$. Two line segments are said to be connected if they share an endpoint. Given a set of line segments $U$, we say that a geometric figure (“...
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Find The Root Description: There is a full binary tree $T$ of size $n > 1$. Recall that a full binary tree is a binary tree in which every node has either $0$ or $2$ children. Let $r$ denote the root of $T$. Note that $T$ qualifies as a full binary tree if and only if it is rooted at $r$. Let $f$ ...
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Find my Family Description: You are looking for a particular family photo with you and your favorite relatives Alice and Bob. Each family photo contains a line-up of $n$ people. On the photo you’re looking for, you remember that Alice, who is taller than you, was somewhere on your left from the per...
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Find the Box Description: Maj is a robotics researcher who works at Lund University. She has learned about a valuable treasure in the cellar of the university. The treasure is in a box located in an empty room deep underground. Unfortunately, Maj cannot just go and look for the box. It is very dark in ...
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Find the Graph Description: Brandon Greg Jr. told you that he found an interesting undirected graph $G$. The graph has $n$ vertices labelled with the integers $1, 2, \ldots , n$. The graph is simple, meaning that each edge is between two distinct vertices, and no two edges are between the same ...
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Finding An A Description: In this problem, you are given a single string $s$ that is guaranteed to contain the letter a. You should output the suffix of $s$ that begins with the first occurrence of the letter $a$. Namely, if $s$ consists of characters $s_1s_2\ldots s_ n$ and $i$ is the first index ...
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Finding Keys Description: Wolfgang Amadeus Mozart has too many keys! He has $n$ keys of distinct lengths on his circular keychain. Unfortunately, Wolfgang can only judge whether a key fits into a door by its relative size compared to the keys surrounding it. Let the $k$-pattern of a key $x$ be the sequ...
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Finding Laputa Description: Pazu and Sheeta are on their quest to the island of Laputa, an ancient floating city shrouded in mystery. Sheeta’s crystal necklace reveals a complex network resembling a hypercube — a mathematical structure they need to navigate to reach Laputa sooner. The hypercube is an ...
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Finding Lines Description: Annabel and Richard like to invent new games and play against each other. One day Annabel has a new game for Richard. In this game there is a game master and a player. The game master draws $n$ points on a piece of paper. The task for the player is to find a straight line...
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Finding Polly Description: Where is Polly Polygon? She’s somewhere in the midst of a field of lines. Given a set of lines, count how many non-self-intersecting polygons can be formed with exactly one segment from each line. Trivial segments (i.e., length 0) do not count. The polygon must contain exact...
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Finn the Giant Description: Frustrated by his legendary inability to tear down Lund’s Cathedral, Finn the Giant wants to become better at destroying pillar-borne edifices. Together with his fellow trolls he has constructed a training site consisting of a colonnade of various pillars supporting a roof. ...
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Fire Description: You are trapped in a building consisting of open spaces and walls. Some places are on fire and you have to run for the exit. Will you make it? At each second, the fire will spread to all open spaces directly connected to the North, South, East or West side of it. Fortunately, walls w...
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Fire Description: In the old Baltic religion, it is important to have a holy fire burning. A priest called krivis is responsible for protecting it from extinguishing. He has many trustworthy helpers called vaidilutės, and wants to create a schedule for them to stoke and protect the fire. He has to ...
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Fire Exits Description: The local museum is facing a huge problem. After years of expansion it now holds a large number of exhibition halls. The halls are connected pairwise by a number of two-way corridors, such that there is exactly one sequence of corridors leading from the entrance to each hall. Du...
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Fire Hydrant Description: Firefighter Robert has been working as a firefighter for over 20 years and loves his job. After a long walk in the metropolis M (formerly known as Stockholm), Robert received a call on his phone from his hydrophobic chief, ordering him to come to the fire station right away. R...
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Fire Station Description: A city is served by a number of fire stations. Some residents have complained that the distance from their houses to the nearest station is too far, so a new station is to be built. You are to choose the location of the fire station so as to reduce the distance to the nearest ...
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Fire! Description: Joe works in a maze. Unfortunately, portions of the maze have caught on fire, and the owner of the maze neglected to create a fire escape plan. Help Joe escape the maze. Given Joe’s location in the maze and which squares of the maze are on fire, you must determine whether Joe can exit t...
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Firefly Description: A Japanese firefly has flown into a cave full of obstacles: stalagmites (rising from the floor) and stalactites (hanging from the ceiling). The cave is $N$ units long (where $N$ is even) and $H$ units high. The first obstacle is a stalagmite after which stalactites and stalagmites ...
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Firetrucks Are Red Description: This shows that her friends are all connected—either directly or indirectly—by numbers. But she still has to convince her family as well as her coworkers. Given a group of $n$ individuals, and a set of numbers that describe each individual, help Lily come up with a proo...
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Firing the Phaser Description: You start charging the phaser beam and retrieve the room layout of the flagship from the archives. You are situated directly above the enemy, from where the layout of the flagship can be modeled by a two-dimensional map of the rooms of the flagship. In this map, each room...
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First Last Description: Alice and Bob are playing a word game. They start with a list of words, and they alternate turns. Alice goes first; she chooses a starting word from the list. On each subsequent turn, the current player must choose a word from the list that starts with the same letter that ends ...
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First Orchard Description: First Orchard is a cooperative game for children 2 years and up. In this simple game, the players pick colored fruits from trees in an orchard and place them into a basket. To make the game more interesting, a raven tries to reach the orchard to steal the fruits. If the playe...
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First of Her Name Description: In the Royal Family, names are very important! As the Royal Historian you have been charged with analyzing the patterns in the names of the Royal Ladies in the realm. There have been $n$ Royal Ladies, for convenience numbered from $1$ to $n$. The name of each Lady is an ...
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Fishing Contest Description: At point $(x, y)$, fish first appear at second $t_{x, y}$ and disappear just before time $t_{x, y} + k$ seconds. Outside of this time, no fish can be caught at this position. It takes no time to catch all the fish at a point, and all points contain the same amount of fi...
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Fishmongers Description: You fish fish. You hate fish. You love monies. Therefore sell fish. To fishmongers. For maximum profit. ## Input The first line of input contains two integers $n$ ($1 \leq n \leq 100\, 000$), the number of fish you have to sell, and $m$ ($1 \leq m \leq 100\, 000$), the n...
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Fitting Cans Description: ScrollBar sells a wide range of exotic beers, which all come in cans of an equally wide range of heights. Luckily, all beer cans have the same width; exactly 66 millimeters. All of the beer cans must be on display, so the customers can choose the right beer. The display case w...
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Fixing Fractions Description: Following the patterns, we conclude that the following equation should also be true: However, this is actually wrong in boring old standard maths. Therefore, we define a new kind of funky maths where it is allowed to cancel out digits on the left side of the equality sign...
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Fixing the Bugs Description: Being bugs, you are not exactly certain how to fix them, even though you have some ideas. For each bug you are able to estimate your ability to quickly fix the bug. Of course, these estimates may be wrong, so if you try to fix a bug and fail, you will revise the estimate of...
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Fizz Buzz Description: Everybody loves easy problems. And no problem is easier than the Fizz Buzz problem. Indeed, F in Finals stands for Fizz Buzz! Let $F_0$ denote the following string: ``` F_in_Finals_stands_for_Fizz_Buzz! ``` We can recursively generate $F_ i$ (for $i \geq 1$) with the following ...
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FizzBuzz Description: Basically, this is how it works: you print the integers from $1$ to $N$, replacing any of them divisible by $X$ with Fizz or, if they are divisible by $Y$, with Buzz. If the number is divisible by both $X$ and $Y$, you print FizzBuzz instead. Check the samples for further clarificati...
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FizzBuzz Description: A company is hiring a software engineer to a top secret job. After a lot of headhunting they now have $N$ candidates left, denoted $1$ to $N$ after anonymization. To test the skills of the candidates, the company has asked them to implement FizzBuzz. A correct implementation of F...
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Fjöldi Bókstafa Description: The Countess of Counting has for as long as she can remember counted anything and everything, including all the letters in books she reads. Now the Countess wants to be sure she has counted the letters in her most recent reading correctly. ## Input One line with $n$ ASCII ...
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Flag Quiz Description: However, sometimes (actually, most of the time) you can figure out the answer to a quiz question just by looking at the alternatives. Being a low budget show, the underpaid quiz question authors strive to minimize their effort in coming up with the alternatives for each question....
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Flashing Fluorescents Description: You have $n$ lights, each with its own button, in a line. Pressing a light’s button will toggle that light’s state; if the light is on, it will turn off, and if the light is off, it will turn on. The lights change at $1$ second timesteps. You can press a button at...
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Flatbökuveisla Description: Ómar recently ordered pizzas. After a short wait the doorbell rings. He opens the front door and before his eyes lie boxes marked with Flýtibaka. He grabs the boxes and places them on the dining table, then calls out loudly and clearly that the food has arrived. All the resi...
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Flatland Fidget Spinner Description: Freddy the Flatland Photographer wants to report on fun new things in Flatland for the Flatland Financial Times. He saw a really nice picture of a Fidget Spinner in Flatland Weekly, and he would like to publish a similar picture. Actually, he likes the picture so mu...
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Flatland Olympics Description: Since this morning e-mails have been filling up your inbox, containing complaints about obscured views during the most important race: the $100$-meter dash. They demand their money back, or threaten exposing you on social media. To make things worse, spectators have not j...
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Fleecing the Raffle Description: Naturally, it is against the raffle rules to put your name in the box more than once. However, it is only cheating if you are actually caught, and since not even the raffle organizers want to spend time checking all the names in the box, the only way you can get caught ...
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Flexible Spaces Description: Golomb Industries is designing their new office building following modern principles that allow for flexible, reconfigurable meeting spaces. Their plans include a very wide rectangular room, with a series of optional parallel partitions. Figure 1 illustrates such a room ha...
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Fleytitala Description: Friðrik is killing time by skipping stones. He’s getting so good at it that he can decide how often the stone will bounce. Friðrik starts by throwing the stone $d$ meters. After each bounce the distance the stone travels is cut in half. How many meters does the stone travel in ...
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Flight Collision Description: The drones are equipped with a sophisticated system that allows them to fly evasive manoeuvres whenever two drones come close to each other. Unfortunately, a software glitch has caused this system to break down and now all drones are flying along the route with no way of a...
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Flight Plan Evaluation Description: When flying between two places, constructing a good flight plan is important. In general there is a wide range of different factors to consider, the most important being fuel consumption and weather forecasts (especially winds). In this problem, we will evaluate flig...
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Flight Planning Description: The airline company NCPC Airways has flights to and from $n$ cities, numbered from 1 to $n$, around the entire world. However, they only have $n - 1$ different flights (operating in both directions), so in order to travel between any two cities you might have to take se...
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Flight Plans Description: As you are probably aware, flight pricing can sometimes be surprisingly complex. For example, it can often be cheaper to take a much longer flight with several legs instead of flying directly between two airports. One of the reasons pricing seems to be complex is that airlines...
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Flight Safety Description: Safety is an important issue when planning flights. First and foremost, one should of course take every possible measure to make sure that the trip is uneventful and that no incidents occur. But even then, one should always be prepared for the worst and try to make sure that ...
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Flip Five Description: This is a logic puzzle in which you have a square grid of 3$\times $3 cells. Each cell is initially either white or black. When you click on a square it flips, or toggles, the color of that square and the colors of its four immediate north, south, east and west neighbors that...
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Flip Flow Description: For over 600 years, the hourglass has been a well-known timekeeping instrument. An hourglass consists of two glass flasks arranged one above the other which are connected by a narrow channel. Inside the hourglass there is sand which slowly flows from the upper to the lower flas...
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Flipping Cards Description: A player’s turn consists of picking a subset of cards from their hand and laying them on the table. The only rule is that the cards must be placed on the table such that no two cards are showing the same picture. Mike thought this was a very appropriate game to play with hi...
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Flipping Container Description: Normally, you would simply lift up the container using a crane and drop it in its target location. Unfortunately, your crane is broken, and the only way for you to move the container is by carefully flipping the container over one of its bottom four edges, resulting in a...
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Flipping Patties Description: Business is booming at Big Bill’s Burger Shack. Bill sells the most convenient, customizable burger in town. Using either the shack’s website or mobile application, customers can request patties that are prepared precisely to the second. The $i$-th order consists of tw...
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Fljúgandi Furðuhlutir Forðast Fókus Description: As is well known, the Earth is of course flat and is monitored by unscrupulous aliens who wish to make sure no one finds out about this secret flatness. To this end the aliens must make sure no one can get a clear picture of their spaceships. The aliens...
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Floating Formation Description: Industrial design students have come up with an amazing idea: they have made some awesome pieces of design and they want to showcase them floating on the water of the IJsselmeer! Unfortunately, their designs do not stay afloat by themselves, so they took a few boats and ...
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Floating Points Description: Your ship has sunk. You want it back. The best way1 to salvage a shipwreck is to release a whole bunch of ping pong balls beneath it. The ping pong balls float up towards the surface, and their buoyancy takes the sunken ship up towards the surface with them. At least, they...
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Floating-Point Format Conversion Description: To help support a patent defense, we need to recover some experimental data that was stored as single precision floating point on a now-defunct Gould Power-Node mini-computer. The Gould used a base 16 floating-point format. We want to convert Gould floating...
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Flood Mapping Description: With global warming and recurring episodes of flooding, it will be important to create flood risk maps that indicate the probability of flooding in any location. Land near a lake can be particularly vulnerable since during heavy rains a lake’s water level may rise and overflo...
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Flood-It Description: Flood-It is a popular one player game on many smart phones. The player is given an $n \times n$ board of tiles where each tile is given one of $6$ colours (numbered $1$–$6$). Each tile is connected to up to $4$ adjacent tiles in the North, South, East, and West directions....
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Flooding Fields Description: Farmer John has a problem: it’s raining, and his pastures are at risk of flooding. Luckily he’s invested in a state-of-the-art drain system that ensures that the water level is the same across the farm. He hasn’t been as lucky with the terrain. Farmer John’s cows can only s...
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Floor Area Description: You are soon going to sell your house, but first, you need to figure out the size of the floor area. It might sound easy, but you have an unused storage room for which you’ve lost the key, and you have no idea how big the storage room is. The only thing in the storage room is a ...
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Floor Plan Description: You are an architect and you have just been appointed to build a new swimming hall. The organisation behind these plans has acquired funding for a swimming pool and surrounding building as large as they want, but unfortunately they could not find anyone willing to pay for the fl...
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Floppy Music Description: Your friend’s newest hobby is to play movie theme songs on her freshly acquired floppy drive organ. This organ is a collection of good old floppy drives, where each drive has been tampered with to produce sound of a unique frequency. The sound is produced by a step motor that ...
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Flow Finder Description: Last summer, Carla the Cartographer went on an expedition on behalf of the National Center for Positioning and Charting (the NCPC). The goal was to measure water flows of a river system far away in the north. However, the area is quite remote and Carla is not the adventurous ty...
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Flow Free Description: Flow Free is a puzzle that is played on a 2D grid of cells, with some cells marked as endpoints of certain colors and the rest of cells being blank. To solve the puzzle, you have to connect each pair of colored endpoints with a path, following these rules: * there is a path connect...
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Flow Layout Description: A flow layout manager takes rectangular objects and places them in a rectangular window from left to right. If there isn’t enough room in one row for an object, it is placed completely below all the objects in the first row at the left edge, where the order continues from left ...
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Flow Shop Description: $N$ swathers have been ordered and there are $M$ stages in the manufacturing process. The swathers will each go through the same sequence of stages. In particular, the processing occurs as follows: For each swather $i$ and each stage $j$, it takes $P_{i,j}$ units of time to ...
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Flower Garden Description: Due to the high cost of flowers in Alberta, Yraglac decided it would be a good idea to plant his own flower garden instead of buying flowers for his girlfriend. We can model his flower garden on a two-dimensional grid, where the position of each flower is given by an $(x,y)$ ...
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Flower Pots Description: Freddy is planning a garden party for this weekend. Many old classmates are going to pay him a visit and Freddy is thinking about some elegant and unexpected improvement of his small horticultural oasis. Inspired by the creations in his favorite gardening journals he decided to...
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Flowery Trails Description: In order to attract more visitors, the manager of a national park had the idea of planting flowers along both sides of the popular trails, which are the trails used by common people. Common people only go from the park entrance to its highest peak, where views are breath...
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Flowing Fountain Description: Last week, Bill filled a champagne fountain for the first time. Delighted by the champagne pouring from one glass into another, he decided that he wants to organize an even bigger champagne fountain for the next World Finals. He already ordered $n$ glass bowls with dif...
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Fluffy Cat Description: You are working on your new mobile game Fluffy Cat. With simple yet engaging game play, it will surely become a top mobile game! In this game, a single player controls a cat in an infinite grid. There is a mouse hidden somewhere in this grid. To win the game, the player must catch ...
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Flugvallakóðar Description: Airports are known by two types of codes: IATA and ICAO. As an example the airport in Keflavík has the IATA code KEF and the ICAO code BIKF. In Absurdistan however there are no international standards in use, everything has to be domestic and be originally made in Absurdist...
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Fluortanten Description: Björn and $n-1$ other children stand in line to meet the "fluortant" (the fluoride administrator, who comes to school to give children fluoride treatments). Different children are more or less scared of the fluortant. The children are numbered from $1$ to $n$, and child $i$ is ...
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Fly Swatter Description: What are your chances of hitting a fly with a tennis racquet? To start with, ignore the racquet’s handle. Assume the racquet is a perfect ring, of outer radius $R$ and thickness $t$ (so the inner radius of the ring is $R-t$). The ring is covered with horizontal and vertical strin...
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Flygildi Description: The webstore Amazon has in the last few years been planning a new way to deliver packages to customers using drones1. When the new delivery system is up and running customers will be able to get their deliveries within just a few hours rather than a few days. Each drone gets a few pa...
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Flygskam Description: To calculate the best route you models the planet as a perfect sphere and assumes that all flights fly at the distance $6381$ km from the center of the earth. The amount of shame for a single point-to-point flight is calculated as the distance between the airports in km, plus ...
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Flying Safely Description: To limit the trust issues you are asked for help. Given the flight schedule, figure out the smallest set of pilots that need to be trusted, such that the spy can safely travel between all cities. ## Input On the first line one positive number: the number of test cases, at m...
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Flæðasmíði Description: The summer is being used to do all kinds of maintenance and the utilities are no exception. There are $n$ sources of water that have been found that need to be connected to $m$ customers. Each source provides exactly $1 \mathrm{L/s}$, and conveniently enough, the pipes can trans...
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Flýtibaka Description: Ómar is ordering pizza for his family. He is very lazy and therefore wants to minimize the time and effort put into ordering the pizza. He doesn’t care what toppings go on the pizza as long as the basics are there: bread, cheese and sauce. Luckily there is a service which suits Ó...
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Fog Catchers Description: For many people, the word “Peru” conjures up images of the Inca temple Machu Picchu and llamas. But for some visitors to the country, even more remarkable is the sight of fog-catching nets, or atrapanieblas, that Peru is using to harvest water from dense fogs. These nets c...
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Folded Map Description: Freddy’s garden became so large that he needs a map to keep evidence of which vegetables are planted in what area. He ordered a high-quality map from the International Cartographic Publishing Company (ICPC). Since the map has a large scale, it does not fit onto a single page and...
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Folding a Cube Description: It is well known that a set of six unit squares that are attached together in a “cross” can be folded into a cube. But what about other initial shapes? That is, given six unit squares that are attached together along some of their sides, can we form a unit cube by folding this ...
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Folding the Paper Description: The software company SoDr is a major vendor of large software systems. One very important part of each such system is the User’s Manual. SoDr recently purchased a User’s Manual Generating Device (UMGD) to generate all the needed manuals automatically. The UMGD consists of...
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Follow the Bouncing Ball Description: There are several games you can download on your phone that are variations of the following idea. The screen is filled with various convex geometric objects each with a number inside. At the bottom of the screen is a gun which fires $n$ balls in a rapid-fire manner whe...
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Font Description: Little Ivica got himself a summer job at a company that produces computer fonts. The branch of the company where Ivica works at specialises in testing computer fonts and Ivica’s team is responsible of testing only lowercase letters of the English alphabet. The letters are tested so t...
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