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apps_data_3500
Bingo is a game of chance played by a group of players. Each player has his or her own bingo card with a $5$-by-$5$ grid of numbers. Each number appears at most once per card. The bingo caller calls out a sequence of randomly drawn numbers, and the players mark the numbers that appear on their card as they are called o...
apps_data_3501
Jaap, Jan, and Thijs are on a trip to the desert after having attended the ACM ICPC World Finals 2015 in Morocco. The trip included a camel ride, and after returning from the ride, their guide invited them to a big camel race in the evening. The camels they rode will also participate and it is customary to bet on the r...
apps_data_3502
Cars! Where do they come from? Where do they go? Nobody knows. They appear where roads have been built, as if out of nowhere. Some say that no two cars are alike. Some say that if you look closely, you can see the pale ghosts of miserable humans inside them, trapped forever—particularly in the morning and late afternoo...
apps_data_3503
Ellen is teaching elementary math to her students and the time for the final exam has come. The exam consists of $n$ questions. In each question the students have to add ($+$), subtract ($-$) or multiply ($*$) a pair of numbers. Ellen has already chosen the $n$ pairs of numbers. All that remains is to decide for each...
apps_data_3504
You’ve heard of acid rain but have you heard of antimatter rain? Antimatter rain is so potent that when it comes into contact with another object, it immediately disintegrates both itself and the object. Kayla’s job as a SpaceFleet Researcher is gathering weather data on exotic planets. This time, their assignment is t...
apps_data_3505
Given $N$ integers in the range $[-50000, 50000]$, how many ways are there to pick three integers $a_ i$, $a_ j$, $a_ k$, such that $i$, $j$, $k$ are pairwise distinct and $a_ i + a_ j = a_ k$? Two ways are different if their ordered triples $(i, j, k)$ of indices are different. -----Input----- The first line of input...
apps_data_3506
One of the perhaps most important factors in deciding the winning team of a football match is the amount of cheers the teams get from their supporters. The Sportify football team is about to meet their worst opponent, Spoilify. As the manager of Sportify’s cheerleading squad, you have to decide on a cheerleading tactic...
apps_data_3507
The host university is organizing a party for this year’s ACM/ICPC contestants with a buffet dinner and $R$ boxes of red wine and $W$ boxes of white wine. Wine boxes are to be arranged into non-empty piles, each pile contains only one type of wine, either white or red. After that, those piles are put into a line so tha...
apps_data_3508
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. The pillars differ in structural strength—som...
apps_data_3509
Richard and Janet are going on their first date. Richard has offered to meet her at home with his bicycle, and Janet tells him she will call when she is ready in $10$ to $20$ minutes. But Richard is an impatient person; while he could wait at home for Janet’s signal, he might also leave early and travel around the neig...
apps_data_3510
Alice and Bob are playing a board game. The board is divided into positions labeled $a, b, c, d, \dots $ and the players use a gamepiece to mark the current position. Each round of the game consists of two steps: - Alice makes a choice. Depending on the current position, she has different options, where each option is...
apps_data_3511
The game Pokenom Go has just been released. Pokenom trainers can now travel the world, capture Pokenom in the wild and battle each other! Bash — the Pokenom trainer — has decided to drop out of his university to pursue his childhood dream of becoming the best Pokenom trainer! However, Linux — Bash’s university headmas...
apps_data_3512
Chances are that you have probably already heard of the travelling salesman problem. If you have, then you are aware that it is an NP-hard problem because it lacks an efficient solution. Well, this task is an uncommon version of the famous problem! Its uncommonness derives from the fact that this version is, actually, ...
apps_data_3513
You are playing the following simple game with a friend: - The first player picks a positive integer $X$. - The second player gives a list of $k$ distinct positive integers $Y_1, \ldots , Y_ k$ such that $(Y_1+1)(Y_2+1) \cdots (Y_ k+1) = X$, and gets $k$ points. Write a program that plays the second player. -----In...
apps_data_3514
You are a seasoned Fight Club member who recently stumbled upon the classified plans of Project Mayhem, a secret organization that the other members have created to bring down consumerism and corporate America. To completely destabilize modern civilization, Tyler Durden and his Project Mayhem trainees are making plans ...
apps_data_3515
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 rather one-dimensional country, and can be represe...
apps_data_3516
The classic video game “Prince of Python” comprises $n$ levels, numbered from $1$ to $n$. You are going to speedrun this game by finishing all of the levels as fast as possible, and you can beat them in any order that you want. You enter each level equipped with one of $n+1$ magical items. In the beginning you only ha...
apps_data_3517
BAAS Inc. (Build Airplanes As-a-Service) has grand plans to build lots of airplanes. Naturally, the airplane construction process consists of multiple steps, each of which may take some time. Some steps can take more time to complete than others, e.g. attaching a plane wing may take longer than spray-painting the BAAS ...
apps_data_3518
This is a very exciting week for John. The reason is that, as a middle school teacher, he has been asked to dedicate the entire week to teaching his class of $n$ students about the cause and effect of global warming. As John is very passionate about his planet, he’s going to spend extra time and effort to make this wee...
apps_data_3519
The game of Memory is played with $N$ pairs of cards where each pair has the same picture, i.e. there are $N$ different pictures, and each of them appear on exactly two cards. The cards are shuffled and placed face down on a large table. On each turn you flip two cards of your choice face up. If they match you remove ...
apps_data_3520
Everyone wants to live as long a life as possible. As time progresses, technology progresses. Various anti-aging pills get introduced to the market at various times which allow a person to age more slowly than normal. In particular, an $x$-$y$ pill, when taken regularly, ages your body only $y$ seconds over the course ...
apps_data_3521
You are planning to travel in interstellar space in the hope of finding habitable planets. You have already identified $N$ stars that can recharge your spaceship via its solar panels. The only work left is to decide the orientation of the spaceship that maximizes the distance it can travel. Space is modeled as a $2$D ...
apps_data_3522
You are building advanced chips for machines. Making the chips is easy, but the power supply turns out to be an issue since the available batteries have varied power outputs. Consider the problem of $n$ machines, each with two chips, where each chip is powered by $k$ batteries. Surprisingly, it does not matter how muc...
apps_data_3523
When Per was living in New York, he couldn’t use his debit card as often as in Sweden. He had to carry cash all the time and his wallet was getting heavy from all the coins he was carrying around. He was once in a candy store buying a few kilos of candy and he wanted to get rid of as many coins as possible but couldn’t...
apps_data_3524
Anthony has two multiple choice assignments to hand in today. The answer to each assignment is a string, where the $i^\textrm {th}$ letter represents the answer to the $i^\textrm {th}$ question. But instead of handing in two strings, Anthony only hands in a single string. He claims he answered every question correctly...
apps_data_3525
The home office of Labyrinthian Inc. has installed a new system of security badges and electronic door locks. Each badge is assigned an ID number, and the idea was that electronic locks on each door should allow access only to personnel whose ID number indicated that they had appropriate security clearance to enter tha...
apps_data_3526
Bob is completing a true/false worksheet, consisting of a list of $n$ problems where each answer is either “true” or “false”. The problems are numbered from $1$ to $n$. They are too hard for Bob, so the TA, Alice, has given Bob $m$ hints. For each hint $i$, Alice gives Bob an (inclusive) range of questions $[l_ i, r_ i...
apps_data_3527
One day your boss explains to you that he has a bunch of computer networks that are currently unreachable from each other, and he asks you, the cable expert’s assistant, to adjoin the networks to each other using new cables. Existing cables in the network cannot be touched. He has asked you to use as few cables as pos...
apps_data_3528
Mirko found a wooden board and $N$ nails in his attic. Mirko hammered the nails into the board as fast as possible. The board can be modeled by a coordinate plane and the nails as points in it. No two nails have the same $x$- or the same $y$-coordinate. In order to keep having fun, Mirko stole his sister’s elastic hai...
apps_data_3529
Given an undirected, unweighted, connected graph, where each edge is colored either blue or red, determine whether a spanning tree with exactly $k$ blue edges exists. -----Input----- There will be a single test case in the input. Each test case will begin with a line with three integers: $n \ m \ k$ Where $n$ ($2 \l...
apps_data_3530
Jimmy and his friends like to visit large theme parks. In the current theme park there are many roller coasters which then are categorized by Jimmy. He assigns a fun value to each coaster; however, the fun decreases with each run. More formally: for a specific roller coaster $i$, Jimmy assigns two fun coefficients $a_...
apps_data_3531
Your state has just purchased a large, unspoiled tract of land, and wishes to turn it into a nature park with hiking trails. The land has $n$ places of interest to which guests may wish to hike, and of these, $k$ are very special. The state wishes to connect these places with hiking trails. There are $m$ candidate hiki...
apps_data_3532
Mirko likes to play with strings of characters, but this time he has taken it too far – he put an “explosion” in the string! An explosion is a series of characters which, if found in the vicinity of fire, explodes and starts a chain reaction. Mirko, being as negligent as he usually is, forgot that his string contained...
apps_data_3533
In a single day, $N$ of Luka’s trucks travel a specific highway. The highway has a number of exits and entrances. An exit with a particular number is in the same location as the entrance with that number. Upon entering the highway, a truck driver receives a ticket which indicates the entrance he used. When exiting, th...
apps_data_3534
Young Mirka is an amateur musician. She plays the multi-piano. $A$ multi-piano consists of an infinite number of multi-keys, denoted with integers that can be interpreted as the pitch. $A$ multi-composition (a composition written for a multi-piano) can be represented with a finite array of integers, where integers deno...
apps_data_3535
Matthew the physicist studies the quantum electro-dynamics of a silicon-based rectangular microchip. The microchip consists of a very large $N \times M$ grid of electrons. Each electron has either positive (up) or negative (down) spin, denoted by $+$ and $-$ respectively. Matthew does not know the spin of all the elec...
apps_data_3536
Consider a rooted tree with $n$ nodes, numbered $1..n$. Each node will have a fixed integer $b$, and for each, a uniform random real number is chosen in the interval $[0..b]$. What is the probability that the random numbers chosen cause the tree to form a Heap (i.e., the random value in each node is less than the rand...
apps_data_3537
David is looking to book some travel over the world. There are $n$ countries that he can visit, and $m$ flights that are available. The $i$th flight goes from country $a_ i$ to country $b_ i$. It departs at time $s_ i$, and lands at time $e_ i$. David is currently at the airport in country $1$, and the current time i...
apps_data_3538
A set of frogs have accidentally fallen to the bottom of a large pit. Their only means of escaping the pit is to jump out of it. Each frog $i$ is described by three parameters $(l_ i,w_ i,h_ i)$ where $l_ i$ is its leap capacity, $w_ i$ its weight, and $h_ i$ its height. The leap capacity specifies how high that frog c...
apps_data_3539
A Bipartite Graph is an undirected graph whose vertices can be partitioned into $2$ sets such that, for each edge $(u, v)$, $u$ and $v$ belong to different sets. Socket has challenged Bash to a Bipartite Battle. In the Bipartite Battle, Bash and Socket play a game with Bipartite Graphs. The Bipartite Battle happens a...
apps_data_3540
You are given a puzzle that can be represented as a $4 \times 4$ grid of colored cells. The solved puzzle contains 4 monochromatic rows, in this order: red, green, blue, yellow. Although we will analyze this puzzle using its 2D representation, it is actually a 3D puzzle! Imagine that the grid is stretched over a torus ...
apps_data_3541
Alf and Beata were two kids who lived long ago, during the time before you could spend Halloween participating in programming competitions. As such, their lives were much more boring than the lives of kids today. How can you survive without programming competitions, you may ask yourself. The answer is easy: you go tric...
apps_data_3542
When constructing electric circuits one has to connect pairs of points using wire, preferable as short as possible. In this problem we have an empty circuit board of size $N \times M$ where we want to connect the two points $A_1$ and $A_2$ with each other using one wire, and the two points $B_1$ and $B_2$ with each oth...
apps_data_3543
Typing on phones can be tedious. It is easy to make typing mistakes, which is why most phones come with an autocorrect feature. Autocorrect not only fixes common typos, but also suggests how to finish the word while you type it. Jenny has recently been pondering how she can use this feature to her advantage, so that sh...
apps_data_3544
People are going to the movies in groups (or alone), but normally only care to socialize within that group. Being Scandinavian, each group of people would like to sit at least one space apart from any other group of people to ensure their privacy, unless of course they sit at the end of a row. The number of seats per r...
apps_data_3545
Anatoly Cheng McDougal is a typical student in many ways. Whenever possible he tries to cut and paste code instead of writing it from scratch. Unavoidably this approach causes him problems. For example, when he first learned about preorder, inorder and postorder traversals of trees, and was given code for a preorder pr...
apps_data_3546
David is writing an article for the Bulletin of the Association of Proof Completions. In his article, he proves several theorems. For every theorem, David came up with a proof. Since David is a very eager student, he even came up with multiple proofs for some of the theorems. As usual, a proof for a theorem may depend ...
apps_data_3547
A dishonest landowner is selling off plots of land. He’s selling it in large, rectangular plots, but many of the plots overlap, so he’s actually selling the same land multiple times! It’s not real estate, it’s unreal estate! Given a description of the possibly overlapping rectangular plots of land that the dishonest l...
apps_data_3548
Pia is a famous bartender at the hip Stockholm night club Supernova. One of her most impressive feats is the mixing a series of drinks using each of the $N$ distinct drink ingredients in the bar exactly once. She does this in the following way. First, Pia chooses a number of drinks to make. Each of the drink ingredien...
apps_data_3549
After your boat ran out of fuel in the middle of the ocean, you have been following the currents for 80 days. Today, you finally got your radar equipment working. And it’s receiving signals! Alas, the signals come from the “radar” station owned by the eccentric lighthouse keeper Hasse. Hasse’s radar station (which doe...
apps_data_3550
In the 21st century, Hunters are expected to master programming languages, in order to effectively gather information on the Internet. Gon is currently learning NenScript — the most popular programming language amongst Hunters. Today, Gon is learning variables. In NenScript, a variable always stores a string of zero ...
apps_data_3551
Dino loves ice cream. In case he ever run out of ice cream at his office, he keeps a stash of dry ice in order to quickly make new ice cream. His recipe for making ice cream includes exactly $T$ liters of dry ice. Unfortunately, he has no marked containers in his office. Instead, he keeps a set of bottles of known tot...
apps_data_3552
The enemy and their massive army is approaching your fortress, and all you have to defend it is a legion of guardian gnomes. There is no hope of winning the battle, so your focus will instead be on causing as much damage as possible to the enemy. You have $n$ gnomes at your disposal. Before the battle, they must be d...
apps_data_3553
“Hey! I have an awesome task with chameleons, $5$-th task for Saturday’s competition.” “Go ahead…” (…) “That’s too difficult, I have an easier one, they won’t even solve that one.” “You are given an array of $N$ integers from the interval $[1, K]$. You need to process $M$ queries. The first type of query requires y...
apps_data_3554
Once upon a time there was a Three-Headed Monkey who had a large stash of banana smoothie on one side of the forest. However, her family lived on the other side of the forest. Our dear monkey wants to suprise them and bring them as much banana smoothie as possible. Unfortunately, having three heads consumes a lot of ...
apps_data_3555
Your dog Spot is let loose in the park. Well, relatively loose – he is tied to a post with a leash, limiting his movements. Spread around the park are various squeaky toys and other dog paraphernalia, which Spot happily goes after when he sees them. When he gets to a toy he will chew at it for a while until it has beco...
apps_data_3556
Several surveys indicate that the taller you are, the higher you can climb the corporate ladder. At TALL Enterprises Inc., this “de facto standard” has been properly formalized: your boss is always at least as tall as you are. Furthermore, you can safely assume that your boss earns a bit more than you do. In fact, you ...
apps_data_3557
In the dangerous wild west, robbers are attacking a long train with many coaches. Chaos erupts, and the robbers realize that the amount of chaos equals the number of passengers in the train, rounded up to the nearest multiple of $10$. In order to quench the chaos, they therefore decide to kill some passengers by blowin...
apps_data_3558
The mayor has decided that it is high time to implement a new system of television transmitters. The city can be represented as a segment of the length $D$ on which there are buildings of different heights. The width of a building is negligible. On top of some buildings, television transmitters are set, their dimension...
apps_data_3559
A typical strategy in the game Starcraft is to mass up large amounts of low-tier units such as Zerglings, then throw them at your opponent and laugh maniacally as they overwhelm any opposition. However, when both players opt for the same strategy, the result can often become... quick, brutal and messy. Sadly, the game ...
apps_data_3560
Nowadays, there are a lot of unusual people. We won’t go into details, but instead focus on a certain type, to us personally the most interesting people. Of course, we’re talking about barbarians! There are a lot of barbarians, but only a few of them are truly important. This story has $N$ important barbarians, denote...
apps_data_3561
John Doe wants to transport his possessions from one bank of Lake Michigan to the other. His possessions consist of $W$ wolves, $S$ sheep, and $C$ cabbages. The transportation will be carried out using a boat that can hold up to $K$ of these items at the same time. During each step, John can take some items from one ba...
apps_data_3562
It is exam time! You have, of course, been spending too much time participating in various programming contests and have not done much studying. Now you have $N$ subjects to study for, but only a limited amount of time before the final exams. You have to decide how much time to allocate to studying each subject, so tha...
apps_data_3563
Dezider is making a game board for the game of Convexity. He drilled a bunch of holes in a piece of wood. As the name of the game suggests the holes were on the boundary of a convex polygon. After turning over the piece of wood, Dezider froze—he had damaged the famous Picasso lithograph—The Bull No. 8. Now the question...
apps_data_3564
Weenesia is an archipelago of perfectly circular islands in the 2D plane. Many islands have palm trees growing in them, perfectly straight up, so we can represent a tree by a 2D point and a height. We want to build a courier system in the islands, i.e., we want to be able to move any object from any land point to any ...
apps_data_3565
Ticket to Ride1 is a board game for up to $5$ players. The goal of the game is to set up train lines (and to thwart the opponents’ attempts at setting up their train lines). At the beginning of play, each player is assigned four train lines. A player may choose to discard as many of these four assignments as she likes....
apps_data_3566
Oostende Beach is a very long beach located in the north of Belgium. On this beach, there are $n$ huts located along a straight line. People can rent a room in one of those huts to spend their beach vacations together with the other tenants. Every day at lunch time, a food truck drives by to serve fries to the guests....
apps_data_3567
Tira would like to join a multiplayer game with $n$ other players. Each player has a character with some features. There are a total of $k$ features, and each character has some subset of them. The similarity between two characters $A$ and $B$ is calculated as follows: for each feature $f$, if both $A$ and $B$ have f...
apps_data_3568
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 moves the read/write head of the floppy dri...
apps_data_3569
One fateful spring evening Bergur was playing his favorite video game Striker-Count. Bergur is so good at Striker-Count he usually defeats his opponents without breaking a sweat. Therefore he’s been racking his brain for new ways to win with style. He decides to jump in the air, rotate a full circle and shoot one shot ...
apps_data_3570
A common plot device in story-telling is the “All Just A Dream” trope. Typical symptoms of this trope being used are talking lions, main characters dying, yodeling aliens on monocycles, and a general plethora of weird events. Then, of course, someone wakes up and it is revealed that everything that happened during the ...
apps_data_3571
When the first scrollbars appeared on resizable windows during user interface development in the Elder Days, computer graphics were still primitive. Widgets were made with ASCII symbols and text was monospaced. A window displayed a viewport: a part of a much longer text, adjusted to fit the width of the window. The thu...
apps_data_3572
Lukáš really likes orienteering, a sport that requires locating control points in rough terrain. To entertain the NWERC participants Lukáš wants to organize an orienteering race. However, it would be too harsh for the participants to be outdoors in this cold Swedish November weather, so he decided to jump on the new tr...
apps_data_3573
Cesar and Raul like betting and good food, in no particular order. They want to try out a new fancy restaurant and they decided to make a bet – they are going to play a game and the loser pays for dinner. They have a box with $N$ balls. Each ball contains a distinct number between $1$ and $N$. Then, the game proceeds ...
apps_data_3574
Young Luka is about to enter a house with the evil witch Marica inside. As soon as he enters the house, she asks him questions about her array of $N$ numbers. Luka fearfully asks for a clarification of the questions. Marica explains to him that each query consists of two integers $L$ and $R$ which represent the positio...
apps_data_3575
MTR (subway) stations are common meetup locations in Hong Kong. Alice and Bob are going to meet up at one of the MTR stations. They each show up at the meeting spot in one of the stations right at noon, without remembering which station they plan to meet at. Having poor cellphone connection at the stations, they fail t...
apps_data_3576
“The power to arrest­–to deprive a citizen of liberty­–must be used fairly, responsibly, and without bias.” ­–Loretta Lynch. Due to desperation caused by the global financial crisis, you, left with no other options, decided to rob a bank to survive. Unfortunately, while you were able to escape with a small fortune, th...
apps_data_3577
On a faraway planet, strange plants with two stems can be found. Every plant on the planet can be described by three numbers: the $x$-coordinates $L$ and $R$ of the two stems, and the height $H$ at which the stems are connected. The following image depicts a plant with $L=2$, $R=5$ and $H=4$. Every day a new plant gro...
apps_data_3578
Note that this is a bit harder version of the problem foodreview. Frida is a writer for Cosmopolitan who writes restaurant reviews. She enjoys it a lot, but it seems that, throughout the years, she has reviewed all the restaurants on Earth. It’s now time to move one level up; she is going to review the food served by ...
apps_data_3579
Statisticians like to create a lot of statistics. One simple measure is the mean value: the sum of all values divided by the number of values. Another is the median: the middle among all values when they have been sorted. If there are an even number of values, the mean of the two middle values will form the median. Th...
apps_data_3580
The problem is simple. You are given a long sequence of integers $a_1, a_2, \ldots , a_ n$. Then you are given a query consisting of a start index $i$ and a subset of integers $B$. What is the longest consecutive subsequence of the given sequence that starts at position $i$ and contains only integers in $B$? Simple, r...
apps_data_3581
Have you recently visited an arcade? Arcade games seem to have become more boring over the years, requiring less and less skill. In fact, most arcade games these days seem to depend entirely on luck. Consider the arcade game shown in the picture, which consists of different holes arranged in a triangular shape. A ball ...
apps_data_3582
At the new start-up company Gaggle, we have rejected the oppressive corporate structures of old, with all of their managers and subordinates and hierarchies and so on. Instead we have embraced a free and open corporate culture in which all employees (called Gagglers) are in charge of themselves and allowed to roam free...
apps_data_3583
Near the great desert of Byteland lies a technologically advanced kingdom of hamsters. In the year 2020, to protect better their territories, the hamsters have decided to build a great wall surrounding crucial parts of their kingdom. The kingdom of hamsters is represented by a convex polygon with $n$ vertices. Vertice...
apps_data_3584
Note that this is an easier version of the problem fancy Oskar really loves onions. Unfortunately, the onions he loves belong to the local vegetable farmer, Lökas Tomatcek. Since Oskar is very cheap, he simply steals Lökas’ onions from the large, convex, onion field. For obvious reasons, Lökas does not approve of this...
apps_data_3585
You have some bags of coins. Each bag contains exactly $k$ coins. Exactly one bag contains only counterfeit coins (we’ll call this the fake bag), while all other bags contain only real coins. All real coins weigh exactly the same number of grams. All counterfeit coins weigh exactly the same number of grams. You don’t k...
apps_data_3586
Given $S$, a set of integers, find the largest $d$ such that $a + b + c = d$ where $a, b, c$ and $d$ are distinct elements of $S$. -----Input----- The input starts with an integer $1 \le N \le 4000$, the number of elements in $S$. It is followed by $N$ lines containing the elements of $s$, one per line. Each element o...
apps_data_3587
Taboo is a popular party game. In this game one player, the Clue Giver, prompts his/her teammates to guess a keyword by giving clues. The Clue Giver is also given a list of taboo strings that must not appear in the clues. For example, if the keyword is “Bruce Lee”, the famous kung-fu star, then the taboo strings may be...
apps_data_3588
You are an experienced investor who is investing in multiple companies. At the end of the year you are expected to file your taxes, which requires you to track and report the total number of shares you held during any of your trading days during the year. The records you have kept are sorted by company: for each compa...
apps_data_3589
Nikolaj works at a company that sells a large number of products. Each product has a product ID, which is a large integer. For error detection, in particular in connection with manual database entry, it would be useful if each product also had a single “check” digit between $1$ and $9$ that can be quickly computed from...
apps_data_3590
You are given two convex polygons $A$ and $B$. It is guaranteed that $B$ is strictly contained inside of $A$. You would like to make a sequence of cuts to cut out $B$ from $A$. To do this, you draw a straight line completely through $A$ that is incident to one of the edges of $B$, which separates $A$ into two pieces. ...
apps_data_3591
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 perspective of the photographer. Also, Bob who is ta...
apps_data_3592
Peter is co-owner of the incredibly successful Pete and Pat’s Pitas and Pizzas and his sales are on fire! But unfortunately, so is his building, due to carelessly laid delivery boxes placed too close to Pete’s famous wood burning pizza oven. After sifting though the remnants, one of the few things Pete is able to salva...
apps_data_3593
Mirko has a chessboard with $N$ rows and just three columns. Slavica has written an integer on each field. Mirko has $K$ dominoes at his disposal, their dimensions being $2 \times 1$, and has to arrange all of them on the board without overlapping, in a way that each domino covers exactly two fields of the board. He ca...
apps_data_3594
Odd and Even have had their share of fun times playing the good old prime game: They start with an arbitrary natural number, and take turns either adding $1$ or dividing by a prime (assuming the result is still a natural number), and the one to reach $1$ is the winner. However, now that they have a new friend, Ingmari...
apps_data_3595
As captain of your space ship you have never encountered a more fierce enemy than the one you have snuck upon now. You immediately bring out the big phaser cannon hoping to take out the flagship before they discover you. There is no room for mistakes and the shot will have to be perfect if you are to stand any chance a...
apps_data_3596
Arnar is playing his favourite video game Association of Myths. He’s playing a character by the name of Lumen. Lumen has a special ability where she can shoot a laser beam across the entire map killing all enemies it hits. The only drawback is that the beam is rather narrow and Arnar isn’t always sure where the enemies...
apps_data_3597
Your game development studio, Ad Hoc Entertainment, is currently working on a billiards-based app they’re calling Pool Shark. Players face a sequence of increasingly devious pool puzzles in which they need to carefully position and aim a single billiards shot to sink multiple pool balls. You’ve just done the first rou...
apps_data_3598
Instead of worrying about the current hyperinflation you decide to go down to the local bar and have a drink. The prices at the bar are displayed using magnetic signs with numbers printed on them, with each magnet showing one or more digits. For instance, the price of $1106$ megacredits is displayed like this: While...
apps_data_3599
“The Drinking Musicians”, a widely known and popular folk group, are coming to your town. The musicians are known not only by their playing skills, but also their rough character. They never arrive on time, don’t know which town they’re in, and frequently have trouble finding the stage. Additionally, during the concer...