id stringlengths 11 14 | content stringlengths 424 1.17M |
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apps_data_3200 | You are at home and about to drive to work. The road you will take is a straight line with no speed limit. There are, however, traffic lights precisely every kilometer, and you can not pass a red light. The lights change instantaneously between green and red, and you can pass a light whenever it is green. You can also ... |
apps_data_3201 | You are given an array of integers of length $N$. Let $s_1, s_2, \ldots , s_ q$ be the lexicographically sorted array of all its non-empty subsequences. A subsequence of the array is an array obtained by removing zero or more elements from the initial array. Notice that some subsequences can be equal and that it holds ... |
apps_data_3202 | One day Mirko, while he was walking through the high grass, stumbled upon a sequence of $N$ colored marbles. Soon he noticed that if he touches $K$ or more consecutive marbles of the same color, they start to twinkle and then he could wish them to magically vanish, although he doesn’t have to do that immediately (see $... |
apps_data_3203 | Everyone knows of the secret agent double-oh-seven, the popular Bond (James Bond). A lesser known fact is that he actually did not perform most of his missions by himself; they were instead done by his cousins, Jimmy Bonds. Bond (James Bond) has grown weary of having to distribute assign missions to Jimmy Bonds every t... |
apps_data_3204 | 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 automatically open and close the bridge, eliminatin... |
apps_data_3205 | You and your friends have just returned from a beautiful vacation in the mountains of the Netherlands. When on vacation, it’s annoying to split the bill on every expense every time, so you just kept all the receipts from the vacation, and wrote down who paid how much for who. Now, it is time to settle the bill.
You c... |
apps_data_3206 | Zara, an aspiring architect and urban planner, has drawn out what she considers to be the perfect skyline. As Zara is still aspiring she must use her young daughter, Pippa, to test out her designs. In order to test out the designs Pippa must build them out of her building blocks! The building blocks Pippa has have a un... |
apps_data_3207 | On the forest-filled moon of Endor there is, if we are to believe the Guinness Book of Records, the longest stick in the whole galaxy. On that stick of $L$ meters in length there are $N$ cheerful chameleons. Each chameleon is moving along the stick with constant speed of $1\mathrm{m}/\mathrm{s}$ in one of two possible ... |
apps_data_3208 | Rookie Pirate Captain Jack Albatross has secretly laid anchor in a hidden bay not far from Port Wine, the local meeting point for grizzled pirates and denizens of the sea. Disguising as a messenger, you have infiltrated the service of the dreaded legendary Captain Stevie, and you are entrusted with carrying small encry... |
apps_data_3209 | Last year, some of the judges tried to travel to NWERC’10 by train. This turned into a big disaster: on the way there, a fire in a control room caused huge delays, while on the return trip, trains in Bremen were delayed due to a terrorist threat in Hamburg. Of course, these huge delays caused other delays in the train ... |
apps_data_3210 | Alice and Bob are playing Dots and Boxes. The game is played on an $N\times N$ square lattice of dots, and they alternate drawing a line segment between horizontally or vertically adjacent dots that haven’t been connected before. Every time a unit square is formed by four line segments, the player who put down the last... |
apps_data_3211 | In the country of Elecuador, a very strange voting system is used. When it is time for the election, each one of the $n$ citizens will arrive in some order to the voting station. There are only two parties to vote for, conveniently named $1$ and $2$. When arriving to the voting station, a person will vote for one of th... |
apps_data_3212 | Buffalo Bill wishes to cross a $1000 \times 1000$ square field. A number of snakes are on the field at various positions, and each snake can strike a particular distance in any direction. Can Bill make the trip without being bitten?
Assume that the southwest corner of the field is at $(0,0)$ and the northwest corner a... |
apps_data_3213 | Sweet Apple Acres has been infested by evil fruit-hungry bats! The Apple family has called for Twilight Sparkle’s help to get rid of them.
Twilight needs to use a powerful spell to eliminate the threat the bats pose. Poring through the volumes of magic books, she found an ancient spell by the legendary Star Swirl the ... |
apps_data_3214 | Better Documents Inc. is contemplating the next generation of word processors. Now, nearly every word processor includes a Spell Checker. BDI, however, is looking forward to replacing that with a true Typo Checker. We’ve all been caught, after relying on a spell checker, by typing mistakes (“typos”) that just happen to... |
apps_data_3215 | The most common technique for shuffling a deck of cards is called the Riffle or Dovetail shuffle. The deck is split into two stacks, which are then interleaved with each other. The deck can be split anywhere, and the two stacks can be interleaved in any way.
For example, consider a deck with 10 unique cards:
1 2 3 4 ... |
apps_data_3216 | Every (positive) rational number can be expressed as a ratio of two (positive) integers. However, in decimal form, rational numbers often have an infinitely repeating pattern, e.g., $1/7 = 0.142857142857142857$... A convenient way of writing this repeating pattern is to put a bar over the first occurrence of the repeat... |
apps_data_3217 | A $10 \times 10 \times 10$ three-dimensional grid of tightly packed cubic atomic energy cells aboard the starship Fiugtuwf is reporting failures on several of its cells. The ship’s engineer must set up enclosures that will contain all of the cells that are reported to be failing, in order to avoid a meltdown. It is imp... |
apps_data_3218 | You are given a hexagonal grid with $n$ rows, where $n$ is an odd integer. The rows are numbered $1$ to $n$ from top to bottom. The odd-numbered rows have exactly $n$ hexagons, and the even-numbered rows have exactly $n-1$ hexagons. Let’s denote the $j$-th hexagon in the $i$-th row by $(i, j)$.
For example, the below ... |
apps_data_3219 | As you might know, the memory in current computers consists of a sequence of bits and each of these bits can be in two possible states. Megan’s company has now developed a great new memory unit where every bit has three possible states. This would all be great, if it wasn’t for Megan’s boss. The boss wants her to write... |
apps_data_3220 | In the USA, a type of dance called square dance is very popular. Four dancing pairs stand as to form a square. A caller then gives a series of moves that the dancers should perform, moving around on the floor.
American wizards, however, find square dancing a bit simplistic. Instead, they have come up with a kind of da... |
apps_data_3221 | Mr. G is one of the most excellent students in North River High School for Gifted Students. Despite having impressive performance in a programming competition and making it to the next round, he was not totally happy since his best friend did not get such a great achievement. In order to appease the poor girl, Mr. G ha... |
apps_data_3222 | Emil loves his electric moped. He loves it so much that he rides it through rain, snow, wind and ice. Some day, he will be able to fly with it. This weekend, Emil is on a vacation in New York. He has compiled a list of cool places to visit, as well as a list of all one-way streets between these places, and now it is ti... |
apps_data_3223 | Anton, a young mathematician, comes from the cold region that is northern Sweden. He likes it there, since there are a lot of trees. Lately, however, this has made him a bit sad, since he can’t see the forest because of all the trees. Therefore, he has asked you to construct a forest.
Since Anton is a mathematician, h... |
apps_data_3224 | You are given four points in space (i.e. $\mathbb {R}^3$). The points are not coplanar. In other words, there is no plane in space that contains all four points.
It is guaranteed that under such assumption, there exists a (unique) sphere whose surface touches all four points. Find the coordinates of the centre of the ... |
apps_data_3225 | A very popular position has just opened up at Poodle Inc. Candidates have formed a queue while they wait for their turn to be interviewed.
Competition is fierce and each candidate knows that they will not be selected if another candidate is strictly better than them. Every minute, each candidate looks at the resumé of... |
apps_data_3226 | The Newton brothers are planning to rob a bank in the city of Alviso and want to figure out a way to escape the city’s only police car. They know that their car is faster than the police car so if they could just reach one of the highways exiting the city they will be able to speed away from the police.
The police car... |
apps_data_3227 | In Croatia there are $N$ cities connected by $E$ two-way roads. Two large food chains have recently reached an agreement on market sharing. In the middle of each road, exactly one chain will be given rights to build a restaurant.
To ensure the market is shared fairly, each city must have at least one restaurant from e... |
apps_data_3228 | The most adventurous part of skiing is the journey onto the mountain-top, between trees and through clouds, and past all sorts of enchanting views.
Naturally, the skiers at the foot of the lift can hardly wait to take their turns (although they are a little disappointed that the climb will eventually terminate). They ... |
apps_data_3229 | You are participating in a programming contest cup. The cup consists of a series of programming contests, followed by a final at the end of the season for the $15$ top ranked contestants in the cup. With only one contest left to go before the final, you are starting to wonder if your performance in the earlier contests... |
apps_data_3230 | When it comes to trams, a lot of people are civilized individuals who know how to behave in one. However, there are always those few who upon spotting a place to sit will run towards it in supersonic speeds. If they spot more than one place, they always try the closest one first.
Problems arise when two or more such i... |
apps_data_3231 | High school is all about being in the coolest group of friends. Headmistress Umbridge knows this, and she also knows that knowledge is power. She has collected data on all of the $n$ students at the school, asking each of them who they are friends with. Now she has a list of responses, but she is suspicious that some o... |
apps_data_3232 | Consider a string of $N$ letters, where $N$ is an even number. Rearrange the letters such that all $N/2+1$ substrings of length $N/2$ are different.
-----Input-----
A single line containing string $S$ of length $N$, where $2 \leq N \leq 10^5$ and $N$ is even. The string consists of lower-case letters from the English ... |
apps_data_3233 | Brandon Greg Jr. considers an array to be scary if its leftmost element is the median of its elements. Given an array with distinct elements $[p_1, p_2, \ldots , p_ n]$, Brandon wants to count the number of scary subarrays.
A subarray is some contiguous chunk of elements $[p_ l, p_{l+1}, \ldots , p_ r]$ where $l\le r$... |
apps_data_3234 | Consider packing widgets for shipping where widgets cannot be stacked upon each other (2D packing). Each widget has a $1\times ~ l$ footprint and is $1$ unit high.
Boxes are available in any $W$ by $H$ by $1$ size such that $H/2 \leq W \leq 2H$, with $W$ and $H$ being integers. The company wants to minimize the amount... |
apps_data_3235 | You are developing a new app intended to simplify expense-sharing among groups of friends. This app will allow them to keep track of who encountered an expense and how it should be shared with others through the form of IOUs. For instance, if Alice pays for a meal shared with Bob and Carol, and Bob’s and Carol’s shares... |
apps_data_3236 | 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 sequence of distinct mansions, so that every pair of c... |
apps_data_3237 | In order to keep up with the rapid technological advancements, Mr. Panda needs to backup all the data on his computer to allow him to do a full upgrade of his computer. Since the upgrade will take some time, he will peruse the services of the company ACM (Association of Computer Maintenance) that provides storage serve... |
apps_data_3238 | Gold Leaf is a very thin layer of gold, with a paper backing. If the paper gets folded and then unfolded, the gold leaf will stick to itself more readily than it will stick to the paper, so there will be patches of gold and patches of exposed paper. Note that the gold leaf will always stick to itself, rather than the p... |
apps_data_3239 | Pokemon Go has become a recent trend. Zapray becomes immediately addicted to the game after it comes out. Zapray’s Pokemon journey begins with a bag of $100$ Pokeballs. Each time he encounters a Pokemon, he keeps throwing Pokeballs to the Pokemon until he either catches the Pokemon or runs out of Pokeballs. Each Pokeba... |
apps_data_3240 | Binary Town is holding its biennial elections. All $k$ positions on its council are open, and as usual Notnomde and Yraglac are the only ones running for each position.
Having long since abandoned quaint majority voting, Binary Town uses binary voting instead. In binary voting, all $v$ voters can cast any number of ba... |
apps_data_3241 | Melita has just returned from the annual pig slaughter. Don’t worry, this is a regular thing in Croatia. The best part was the abundance of food! There was everything, starting from good spicy sausages, ham, black pudding, up to teewurst, top quality bacon and čvarci, all with warm white bread and butter. After these a... |
apps_data_3242 | Polly, the programming parrot, has escaped. As Johan is in desperate need for some programming skill, he wants to find her. The only clue that Johan has about the escape route is that Polly flew into his kitchen.
Johan has $N$ boxes on his kitchen table, and each box has a certain probability to contain the parrot. Ea... |
apps_data_3243 | A number of regional Internet Service Providers (ISPs), both big and small have recently been forced into a merger by the government, in an effort to improve service for all. Of course this has been decided without consulting you, the chief network infrastructure officer, and a deadline for when the ISPs should be merg... |
apps_data_3244 | Instead of paying attention in class, Luka is killing time playing with numbers again. This time, he wrote $N$ non-negative integers so that they form a ring (circle). After that he formed a new ring by adding to each number its two neighbours.
The teacher noticed this and took away the first piece of paper, with the ... |
apps_data_3245 | You might have heard about the friendly interactive shell - fish. It’s terminal based, but a bit friendlier to new users who can’t remember the commands they typed before. Fish can use your history of commands for command completion: pressing up (“^”) finds the last command you ran that shares the prefix you have alrea... |
apps_data_3246 | It is a well-known fact that if you mix up the letters of a word, while leaving the first and last letters in their places, words still remain readable. For example, the sentence “tihs snetncee mkaes prfecet sesne”, makes perfect sense to most people. If you remove all spaces from a sentence, it still remains perfectly... |
apps_data_3247 | Magnus is the youngest chess grandmaster ever. He loves chess so much that he decided to decorate his home with chess pieces. To decorate his long corridor, he decided to use the knight pieces. His corridor is covered by beautiful square marble tiles of alternating colors, just like a chess board, with $n$ rows and $m$... |
apps_data_3248 | Mirko’s ASCII street is made of $N$ lowercase letters of the English alphabet. The city government occasionally replaces the tiles in the street. However, the letter tiles are in high demand, so the government has only $M$ different tile patterns available.
The $i$th tile pattern consists of $L_ i$ letters. A tile can... |
apps_data_3249 | 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 saved by a system of bulkheads, reinforced ve... |
apps_data_3250 | Most people have heard of Julius Caesar, a Roman dictator who lived in the first century BC and who was famous, amongst other things, for defeating enemies by pitting them against each other, thereby preventing them from uniting against him, a strategy known as “Divide and Conquer”. A lesser known fact is that Julius C... |
apps_data_3251 | Mirko got a set of intervals for his birthday. There are many games he can play with them. In one of them, Mirko must find the longest sequence of distinct intervals such that each interval in the sequence is in the set and that each interval contains the one that follows in the sequence.
Write a program which finds o... |
apps_data_3252 | Your greeting card company makes unique greeting cards. The sizes of these greeting cards vary widely because of the whims of card designers. There are a lot of different types of cards, and each has a specific quantity that you need to manufacture.
Your job is to determine what envelopes to order for these greeting c... |
apps_data_3253 | In a few weeks time, a new president will be elected in the country of Marecia. There are two political parties: the Constituents and the Federals. Each party has one presidential candidate; one of these will become the new president.
This year you are more involved than ever before: you are the candidate for the Cons... |
apps_data_3254 | Slavko decided to challenge Mirko! He gave him a real number $P$ and a bag full of pieces of paper with exactly one number between $1$ and $5$ inclusive written on each paper. There is an unlimited quantity of each type of paper.
Mirko’s task is to pick the minimum number of papers in a way that the average of the num... |
apps_data_3255 | A hopper is a virtual creature that visits Java programs and explores their arrays. Scientists observed a hopper and came to the following conclusions:
- a hopper only visits arrays with integer entries,
- a hopper always explores a sequence of array elements using the following rules:
- a hopper cannot jump too far... |
apps_data_3256 | Barr the Bear is playing the game Bits with Swanky Shen!
Bits is a very simple game. At the start, a circle of $N$ non-negative integers $A_1$, $A_2$, $A_3$, $\ldots $, $A_ N$ is shown to both players. That is, to the left of the integer $A_ i$ is the integer $A_{i-1}$ if $i > 1$; and the integer $A_ N$ otherwise. To ... |
apps_data_3257 | The Algebraist Carpet Manufacturing (ACM) group likes to produce area carpets based upon various geometric figures. The 2014 ACM carpets are all equilateral triangles. Unfortunately, due to a manufacturing defect, some of the carpets are not as stain-resistant as intended. The ACM group is offering to replace each defe... |
apps_data_3258 | Everyone knows that cats love to eat mice. Naturally, when given the opportunity, any cat wants to eat as many mice as possible.
It just so happens that Cartesian Cat lives on the Cartesian Plane with her home located at $(0, 0)$. Obviously, none of the mice live at this location, they are smarter than that! However, ... |
apps_data_3259 | Aladin was walking down the path one day when he found the strangest thing: $N$ empty boxes right next to a weird alien machine. After a bit of fumbling around he got the machine to do something. The machine now accepts 4 integers $L$, $R$, $A$ and $B$. After that hitting the big red glowing button labeled “NE DIRAJ”1 ... |
apps_data_3260 | loglogloglog. Brandon Greg Jr. is sometimes a drowning combinatorist.
A permutation of length $n$ can be represented as some order of the integers $\{ 1,2,\ldots ,n\} $. A run of length $k$ in a permutation is $k$ consecutive elements that appear in increasing or decreasing order. For example, $[5,2,4,3,1]$ is a permu... |
apps_data_3261 | Luka found a very unusual game board in his attic. Surprisingly, it consists of $R \cdot C$ square cells. The rows are numbered $0$ to $R-1$ top to bottom and the columns $0$ to $C-1$ left to right.
What makes the board unusual is the way in which the cells are coloured. Each cell is either grey or white:
- white, if... |
apps_data_3262 | You run a delivery company and must deploy a fleet of vehicles to deliver goods to clients. All of the goods and delivery trucks are initially located at your warehouse.
The road network consists of one-way streets between junctions. The warehouse and clients are all located at a junction. You know the driving time a... |
apps_data_3263 | Fluttershy has been put in charge of a high-end boutique in Manehattan, and she needs to deal with the customers that come in.
It is well-known that Fluttershy is, well, very shy. So shy, in fact, that the only time she feels comfortable dealing with a customer is when she is wearing the same type of clothing as that ... |
apps_data_3264 | Mirko and Slavko are playing a game. Mirko’s turn is first and he chooses a non-empty set of pairs of numbers between $1$ and $N$ (inclusive) under the condition that the numbers that comprise a pair are mutually relatively prime. The numbers that comprise a pair must be different. For example, for $N = 5$, Mirko could... |
apps_data_3265 | Alice and Bob spend this summer planning next year’s summer vacation. They want to travel from the old city of A-town to the popular summer resort B-ville, but they haven’t yet decided which other places to visit en route. There are $N$ places to visit in total, numbered from $1$ to $N$. A-town is place number $1$ and ... |
apps_data_3266 | -----Input-----
The first line of input contains a line with four non-negative integers, $2 \le n \le 500$, $0 \le m \le 10000$, $0 \le s \le n-1$ and $0 \le t \le n-1$, separated by single spaces, where $n$ is the numbers of nodes in the graph, $m$ is the number of edges, $s$ is the source and $t$ is the sink ($s \ne ... |
apps_data_3267 | Mirko and Slavko are playing a chess like game. The game is played on a non-standard chess board sized $R$ rows by $C$ columns. Each player starts with some number of chess kings. In chess kings can move from their current field to any of the $8$ neighbouring fields. Player spread is defined as the complete sum of dist... |
apps_data_3268 | One day, a flock of hungry birds find a huge tree of elderberries. They want to eat all berries of this tree. These birds quickly alight on some leaves of the tree and eat all berries at where they stand. Now they are thinking of who will eat other berries …
Since the flock has some giant birds and some tiny birds, an... |
apps_data_3269 | The distance between two integers is defined as the sum of the absolute result of subtracting their digits. For example, the distance between the numbers 4561 and 3278 is $|4 - 3| + |5 - 2| + |6 - 7| + |1 - 8| = 12$. If one of the numbers consists of fewer digits than the other, we fill it with leading zeroes. Therefor... |
apps_data_3270 | A Word Ladder is a puzzle in which you transform one word into another, by changing one letter at a time. But, there’s a catch: every word that you form in each step must be in the dictionary! Here’s an example of how to transform CAT into GAS:CAT $\rightarrow $ CAR $\rightarrow $ WAR $\rightarrow $ WAS $\rightarrow $ ... |
apps_data_3271 | Consider a sequence of $N$ integers where each integer between $1$ and $N$ appears exactly once.
A pair of numbers in the sequence is confused if the number that comes earlier in the sequence is larger than the later number.
The confusion of the sequence is the number of confused pairs in it. For example, the confusi... |
apps_data_3272 | Hu the Tomb Raider has entered a new tomb! It is full of gargoyles, mirrors, and obstacles. There is a door, with treasure beyond. Hu must unlock the door guarding the treasure. On that door is written, in an ancient tongue, the secret to opening the door:Every face of every gargoyle shall see a face of a gargoyle.
Th... |
apps_data_3273 | You are an archaeologist exploring the underground crypts of Rome. You have just stumbled into a hidden archive containing copies of a lost manuscript by the Knights Templar. Unfortunately, the copies have crumbled over time and now comprise thousands of small text fragments that need to be reassembled in order to rest... |
apps_data_3274 | You have been captured by an evil organization which seeks to exploit your algorithm skills to improve their weapons. The first task they forced you to work on was to program guided torpedoes. Naturally, your goal is to instead make the torpedoes miss every ship whenever possible.
A typical scenario where the torpedo... |
apps_data_3275 | Young Luka is an art dealer. He has $N$ clients and sells artistic paintings to each client. Each client can purchase either colored paintings or black and white paintings, but not both. The client denoted with $i$ wants to purchase at most $a_ i$ colored paintings and at most $b_ i$ black and white paintings. The clie... |
apps_data_3276 | One day you were visiting a museum where you saw a modern piece of art that shows a grid of $N$ rows and $M$ columns. Each cell in the grid has a color, which can be one of the four: red (‘R’), green (‘G’), blue (‘B’), and white (‘W’).
You think that the art is so simple so that even you can reproduce it yourself. Aft... |
apps_data_3277 | We always hope things in our lives will run smoothly, and having smooth arrays may help. An array $A$ of $N$ non-negative integers is $K_ S$-smooth if the sum of every set of $K$ consecutive integers is exactly $S$. Unfortunately, not all arrays are $K_ S$-smooth. In fact, all $K_ S$-smooth arrays must contain a repeat... |
apps_data_3278 | Somewhere in an animal kingdom far from here there is a large forest. Inside the forest live a large number of frogs. Every year the frogs gather along the big central road in the forest to show the other animals their unique ability during the Big Animal Prowess Conference (BAPC).
These frogs are experts in forming ... |
apps_data_3279 | Bar Code is a puzzle game invented by Thinh Van Duc Lai in 2017 that was first published in the New York Times. Bar Code is played on a square grid consisting of $n \times n$ unit squares with $(n+1) \times (n+1)$ grid points. For a given specification, the puzzle requires the marking of some of the borders of these un... |
apps_data_3280 | Ada, Bertrand and Charles often argue over which TV shows to watch, and to avoid some of their fights they have finally decided to buy a video tape recorder. This fabulous, new device can record $k$ different TV shows simultaneously, and whenever a show recorded in one the machine’s $k$ slots ends, the machine is immed... |
apps_data_3281 | My colleague Elisabeth is lazy, both at work and when going to work. She never wants to do more than necessary, which also applies to her journey to work. Her goal is to use a minimum amount of energy, which she achieves by braking and accelerating as little as possible. This method applies to all wheel-based transport... |
apps_data_3282 | Quido has lunch in Hugo’s restaurant every day. He likes the restaurant because all of its prices are expressed as integers, and for each possible price (i.e. $$1$, $$2$, $$3$, etc.) there is at least one beverage and at least one main dish on the menu. Every day there are three entries printed on Quido’s lunch bill: t... |
apps_data_3283 | Gem Island is a tiny island in the middle of the Pacific Ocean. Until recently, it was known as one of the poorest, but also most peaceful, places on Earth. Today, it is neither poor nor peaceful. What happened?
One sunny morning, not too long ago, all inhabitants of Gem Island woke up to a surprise. That morning, eac... |
apps_data_3284 | Given intervals $[a, b]$ and $[c, d]$, count the number of ordered pairs of co-prime integers $(x, y)$ such that $a \le x \le b$ and $c \le y \le d$. Coprime integers have no common factor greater than $1$.
-----Input-----
The input consists of a single line of four space-separated integers $a$, $b$, $c$, and $d$. The... |
apps_data_3285 | A smallest different sequence (SDS) is a sequence of positive integers created as follows: $A_1=r \geq 1$. For $n>1$, $A_ n=A_{n-1}+d$, where $d$ is the smallest positive integer not yet appearing as a value in the sequence or as a difference between two values already in the sequence. For example, if $A_1 =1$, then si... |
apps_data_3286 | Your friend Edvin loves languages. A personal favourite of his is speaking the Robber Language. For those of you not familiar with it, it is a language transformation where every consonant is doubled, with an ’o’ put in-between. The rest is kept the same. For example, the word "car" would be transformed into "cocaror".... |
apps_data_3287 | Two thieves (who strongly “recommended” us not to reveal their names) has broken into the central bank of Logland, where the country’s cash reserve is stored. In Logland, the currency has the $k$ denominations $1, 2, 4, 8, \ldots , 2^{k - 1}$, and the bank currently stores $x_ i$ coins of denominations $2^i$.
Thieves ... |
apps_data_3288 | A string is called double free if no two adjacent letters are the same.
A string is called $k$-incremental if for all values of $j$ in the range $[1,k]$, there exists exactly one character with $j$ occurrences, and the string’s length is $1+2+3+\ldots +(k-1)+k$. For example, if $k=3$, then a $3$-incremental string sho... |
apps_data_3289 | As an employee of the world’s most respected political polling corporation, you must take complex, real-world issues and simplify them down to a few numbers. It isn’t always easy. A big election is coming up and, at the request of Candidate X, you have just finished polling $n$ people. You have gathered three pieces of... |
apps_data_3290 | Today your friends are playing a game of Exploding Kittens. On a player’s turn, she must perform the following actions in order:
- Draw a single card from the top of the deck.
- If the drawn card is an “Exploding Kitten”, she must leave the game unless she has a “Defuse” card in her hand, in which case she must disca... |
apps_data_3291 | You are an employee of the Boxing And Processing Company and you are tasked with distributing boxes in one of the company’s enormous warehouses. At BAPC Ltd., boxes travel by conveyor belt. Two conveyor belts can be merged into one by letting one drop its content onto the other. On the other hand, a belt can be split i... |
apps_data_3292 | Teacher Herkabe has decided to rank his students again. This time, he wants his list to also be aesthetically pleasant, so he has decided that similar names (those beginning with the same letter or sequence of letters) must be close to one another on the list. Therefore, he has devised the following rule:
For every tw... |
apps_data_3293 | Sleazy Bob has happened upon a vending machine. After watching enough people buy tasty snacks, Bob has realized that the vending machine is broken!
Here’s what Sleazy Bob observes:
- A person tries to buy a snack
- The vending machine then checks to see if there are any left of that snack
- If there are any left, t... |
apps_data_3294 | AcmeCorp is always looking to expand its drilling operations.
Their latest target is a largely uninhabited area in the North of the country, known as Crossland. Since the pocket of oil is quite deep already, and new drill bits are expensive, Crossland’s oil company would like to minimise the distance drilled—which may... |
apps_data_3295 | Mirko and his older brother Slavko are playing a game. At the beginning of the game, they pick three numbers $K$, $L$, $M$. In the first and only step of the game, each of them picks their own $K$ consecutive integers.
Slavko always picks the first $K$ integers (numbers $1, 2, \ldots , K$). Mirko has a special demand—... |
apps_data_3296 | You are soon to graduate from the mathemagician school of Hagworts, and you’re quite content with yourself; all the hard work and elbowing has finally paid off. Being successful at most of your endeavors you would normally end up a herald of sound reasoning and good mathemagics. You, however, are different; not only ha... |
apps_data_3297 | You may have seen puzzles, sometimes called cryptarithmetic puzzles, or simply cryptarithms, that look like this:SEND+MORE=MONEY
The goal of this kind of puzzle is to replace each letter with a (base-$10$) digit so that the resulting arithmetic equality holds. Here are the rules:
- A given letter must always be repla... |
apps_data_3298 | You have recently been promoted to lead scientist at NASA, the National Association for Sorting Algorithms. Congratulations! Your primary responsibility is testing the sorting algorithms that your team produces. Fortunately, NASA has a large budget this year, and you were able to buy some state-of-the-art integers you ... |
apps_data_3299 | Consider an $n \times m$ checkerboard. On each cell of the checkerboard, place a positive integer. The values in each column of the checkerboard must be in strictly increasing order from top to bottom, and the values in each row of the checkerboard must be in strictly increasing order from left to right.
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3... |
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