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Piggy-Bank (PIGBANK) Before ACM can do anything, a budget must be prepared and the necessary financial support obtained. The main income for this action comes from Irreversibly Bound Money (IBM). The idea behind is simple. Whenever some ACM member has any small money, he takes all the coins and throws them into a ...
30,700
Lifting the Stone (STONE) There are many secret openings in the floor which are covered by a big heavy stone. When the stone is lifted up, a special mechanism detects this and activates poisoned arrows that are shot near the opening. The only possibility is to lift the stone very slowly and carefully. The ACM team mus...
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Play on Words (WORDS1) Some of the secret doors contain a very interesting word puzzle. The team of archaeologists has to solve it to open that doors. Because there is no other way to open the doors, the puzzle is very important for us. There is a large number of magnetic plates on every door. Every plate has...
30,702
Adding Reversed Numbers (ADDREV) The Antique Comedians of Malidinesia prefer comedies to tragedies. Unfortunately, most of the ancient plays are tragedies. Therefore the dramatic advisor of ACM has decided to transfigure some tragedies into comedies. Obviously, this work is very hard because the basic sense of the pla...
30,703
Copying Books (BOOKS1) Before the invention of book-printing, it was very hard to make a copy of a book. All the contents had to be re-written by hand by so called scribers . The scriber had been given a book and after several months he finished its copy. One of the most famous scribers lived in the 15th century and ...
30,704
Substitution Cipher (SCYPHER) Antique Comedians of Malidinesia would like to play a new discovered comedy of Aristophanes. Putting it on a stage should be a big surprise for the audience so all the preparations must be kept absolutely secret. The ACM director suspects one of his competitors of reading his correspo...
30,705
Commedia dell Arte (COMMEDIA) So called commedia dell' arte is a theater genre first played in Italy at the beginning of the sixteenth century. It was inspired with the Roman Theater. The play had no fixed script and the actors (also called performers ) had to improvise a lot. There were only a simple direction...
30,706
Skyscraper Floors (SCRAPER) What a great idea it is to build skyscrapers! Using not too large area of land, which is very expensive in many cities today, the skyscrapers offer an extremely large utility area for flats or offices. The only disadvantage is that it takes too long to get to the upper floors. Of cour...
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Glass Beads (BEADS) Once upon a time there was a famous actress. As you may expect, she played mostly Antique Comedies most of all. All the people loved her. But she was not interested in the crowds. Her big hobby were beads of any kind. Many bead makers were working for her and they manufactured new necklaces and ...
30,708
Hares and Foxes (HAREFOX) The Antique Comedians of Malidinesia play an interesting comedy where many animals occur. Because they want their plays to be as true as possible, a specialist studies the behaviour of various animals. Recently, he is interested in a binary dynamic ecological system hares-foxes (SHF). As ...
30,709
Invitation Cards (INCARDS) In the age of television, not many people attend theater performances. Antique Comedians of Malidinesia are aware of this fact. They want to propagate theater and, most of all, Antique Comedies. They have printed invitation cards with all the necessary information and with the programme....
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Fake tournament (TOUR) We consider only special type of tournaments. Each tournament consists of a series of matches. We have n competitors at the beginning of a competition and after each match the loser is moved out of the competition and the winner stays in (there are no draws). The tournament ends when there is ...
30,711
Julka (JULKA) Julka surprised her teacher at preschool by solving the following riddle: Klaudia and Natalia have 10 apples together, but Klaudia has two apples more than Natalia. How many apples does each of he girls have? Julka said without thinking: Klaudia has 6 apples and Natalia 4 apples. The teac...
30,712
Jasiek (JASIEK) Jasiek is only 6 years old, but he already has many skills. He likes drawing and asking riddles very much. This morning he got a sheet of grid paper and a pencil from his mother and he started drawing. All his drawings have some common properties: Jasiek colors full grid squares; if some c...
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Dyzio (DYZIO) Dyzio is Jasiek's friend and he also likes riddles. Here is a riddle he came up with: Jasiek, here is a piece of rope, which has to be cut into smaller pieces. I will not tell you directly how to do it, but look at this sequence of zeros (0) and ones (1). A one at the beginning means that the r...
30,714
Supernumbers in a permutation (SUPPER) An n -element permutation is an n -element sequence of distinct numbers from the set {1, 2, ... n} . For example the sequence 2, 1, 4, 5, 3 is a 5-element permutation. We are interested in the longest increasing subsequences in a permutation. In this exemplary permutation ...
30,715
Crime at Piccadily Circus (PICAD) Sherlock Holmes is carrying out an investigation into the crime at Piccadily Circus. Holmes is trying to determine the maximal and minimal number of people staying simultaneously at the crime scene at a moment when the crime could have been commited. Scotland Yard has already carried...
30,716
Bytelandian Information Agency (BIA) Bytelandian Information Agency (BIA) uses a net of n computers. The computers are numbered from 1 to n , and the computer number 1 is a server. The computers are connected by one-way information channels. Every channel connects a pair of computers. The whole network is o...
30,717
The Gordian Dance (DANCE) The Gordian Dance is a traditional Bytelandian dance performed by two pairs of dancers. At the beginning the dancers are standing in the corners of the square ABCD , forming two pairs: A-B and C-D . Every pair is holding an outstretched string. So in the starting position both strings a...
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Brackets (BRCKTS) We will call a bracket word any word constructed out of two sorts of characters: the opening bracket "(" and the closing bracket ")". Among these words we will distinguish correct bracket expressions . These are such bracket words in which the brackets can be matched into pairs such that ev...
30,719
The Imp (IMP) An Imp jumps on an infinite chessboard. Moves possible for the Imp are described by two pairs of integers: (a, b) and (c, d) - from square (x, y) the Imp can move to one of the squares: (x+a, y+b), (x-a, y-b), (x+c, y+d), (x-c, y-d). We want to know for which square different from (0, 0) to which th...
30,720
Square Brackets (SQRBR) You are given: a positive integer n, an integer k, 1 ≤ k ≤ n, an increasing sequence of k integers 0 < s 1 < s 2 < ... < s k ≤ 2n. What is the number of proper bracket expressions of length 2n with opening brackets appearing in positions s 1 , s 2 ... s k ? Illustration Se...
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Permutations (PERMUT1) Let A = [a 1 , a 2 , ... a n ] be a permutation of integers 1, 2, ... n. A pair of indices (i, j), 1 <= i <= j <= n, is an inversion of the permutation A if a i > a j . We are given integers n > 0 and k >= 0. What is the number of n-element permutations containing exactly k inversions? ...
30,722
Ball (BALL1) On the rectangular chessboard of n × m square fields we choose one field adjacent to the edge of the chessboard, called the starting field. Then we put a ball in the center of this field and push it to roll through the chessboard. The diameter of the ball equals the width (and height) of chessboa...
30,723
Cross-country (CRSCNTRY) Agness, a student of computer science, is very keen on cross­country running, and she participates in races organised every Saturday in a big park. Each of the participants obtains a route card, which specifies a sequence of checkpoints, which they need to visit in the given order. Ag...
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Cutting out (CUTOUT) One has to cut out a number of rectangles from a paper square. The sides of each rectangle are to be parallel to the sides of the square. Some rectangles can be already cut out. What is the largest area of a rectangle which can be cut out from the remaining paper? Illustration Three r...
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Expression (EXPR1) We are given an integer k and an arithmetic expression E with the operations '+', '-', and arguments from the set {0, 1 ... 9}. Is it possible to put some parentheses in E to get a new expression E' whose value equals k? If the answer is positive what is the minimum number of pairs of paren...
30,726
Moulds (MOULDS) In a factory, moulds for casting metal objects are produced by a special cutting device. The device is equipped with cuboid-shaped blade of size 1 mm x 1 mm x 30 mm (its height) which operates with each of its sides thus producing the mould from cuboid of size 250 mm x 250 mm x 30 mm (its height)...
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Relations (RELATS1) You are given a directed graph, whose edges are labeled with relational symbols '<', '>' and '='. For a nonnegative integer k, a k-correct G-labeling is a mapping from vertices of G into integers from interval [0,k] such that numbers at the ends of each edge satisfy the relation described ...
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Tree (TREE1) Consider an n-vertex binary search tree T containing n keys 1, 2 ... n. A permutation p = [p 1 ... p n ] of the integers 1, 2 ... n is said to be consistent with the tree T if the tree can be built from the empty one as the result of inserting integers p 1 , p 2 ... p n . Find how many per...
30,729
Bacterial (BAC) In the biology laboratory we are observing several bacterial samples, and under the microscope we have them shaded with different colors to see them expanding their territory on the plate. It is interesting to know that the bacterial are ...
30,730
Editor (EDIT1) Have you ever programmed in Brainf**k? If yes, then you know how annoying it is to press the same key several times in a row. So what we all need, is a good editor. Here are the functions that the editor should have: '\n': begin a new line. If the last line was empty, stop processing and pri...
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Editor Inverse (EDIT2) You are given a text. Calculate the minimum number of keystrokes needed to produce this text, if the editor described below is used. If you haven't read the problem "Editor" before, here is a description of the functionality of the editor: '\n': begin a new line. If the last line ...
30,732
New bricks disorder (BRICKS) You have n bricks arranged in a line on the table. There is exactly one letter on each of them. Your task is to rearrange those bricks so that letters on them create some specified inscription. While rearranging you can only swap adjacent bricks with specified letters (you are given m pair...
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Marbles (MARBLES) Hänschen dreams he is in a shop with an infinite amount of marbles. He is allowed to select n marbles. There are marbles of k different colors. From each color there are also infinitely many marbles. Hänschen wants to have at least one marble of each color, but still there are a lot of possibilities ...
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Easy Problem (EASYPIE) Last year there were a lot of complaints concerning the set of problems. Most contestants considered our problems to be too hard to solve. One reason for this is that the team members responsible for the problems are not able to evaluate properly whether a particular problem is easy or ...
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Bundling (BUNDLE) Outel, a famous semiconductor company, recently released a new model of microprocessor called Platinium. Like many modern processors, Platinium can execute many instructions in one clock step providing that there are no dependencies between them (instruction I 2 is dependent on instructi...
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Shortcut (SHORTCUT) Mirek has a favourite way from home to the university that he traverses every working day. The route consists of sections and each section is a straight segment 10 meters long. Each section is either a straight ahead extension of the previous section or it is perpendicular to the previous ...
30,737
Dice Contest (DICE1) Everyone loves gambling in the Dicent City. Every Saturday the whole community meets to attend a dice contest. They started a few years ago with a classic six-sided die with 1 to 6 dots displayed on the sides and had a lot of fun. However they soon got bored and that's why more soph...
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November Rain (RAIN1) Contemporary buildings can have very complicated roofs. If we take a vertical section of such a roof it results in a number of sloping segments. When it is raining the drops are falling down on the roof straight from the sky above. Some segments are completely exposed to the rain but the...
30,739
Football (FOOTBALL) Eric has a classic football that is made of 32 pieces of leather: 12 black pentagons and 20 white hexagons. Each pentagon adjoins 5 hexagons and each hexagon adjoins 3 pentagons and 3 hexagons. Eric drew a polygon (i.e. a closed line without intersections) along the edges of the pieces. Th...
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Which is Next (TREE2) Every computer science student knows binary trees. Here is one of many possible definitions of binary trees. Binary trees are defined inductively. A binary tree t is either an external node (leaf) or an ordered pair t = (t 1 , t 2 ) representing an internal node with two subtrees ...
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Hang or not to hang (HANGLET) Little Tom is learning how to program. He has just written some programs but is afraid to run them, because he does not know if they will ever stop. Please write a program to help him. This task is not as easy as it may seem, because Tom's programs are possibly not deterministic. Given...
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Minimizing maximizer (MINIMAX) The company Chris Ltd. is preparing a new sorting hardware called Maximizer. Maximizer has n inputs numbered from 1 to n. Each input represents one integer. Maximizer has one output which represents the maximum value present on Maximizer's inputs. Maximizer is implemented as a...
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Two squares or not two squares (TWOSQRS) Given integer n decide if it is possible to represent it as a sum of two squares of integers. Input First line of input contains one integer c ≤ 100 - number of test cases. Then c lines follow, each of them consisting of exactly one integer 0 ≤ n ≤ 10 12 . Output ...
30,744
Cutting off Squares (CUTSQRS) Two players take it in turns to cut off squares from a rectangle. If the lengths of the sides of the rectangle are a and b (a ≤ b) at the beginning of a player's turn, he may cut off as many squares with a side of length a as he likes (but at least 1 square), provided the square he ...
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Numeral System of the Maya (MAYA) The Maya lived in Central America during the first millennium. In many regards, they constituted one of the most developed and most fascinating cultures of this epoch. Even though draught animals and the wheel were unknown to the Mayas, they excelled in the fields of weaving, architec...
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Street Parade (STPAR) For sure, the love mobiles will roll again on this summer's street parade. Each year, the organisers decide on a fixed order for the decorated trucks. Experience taught them to keep free a side street to be able to bring the trucks into order. The side street is so narrow that no two cars can...
30,747
Shopping (SHOP) The old tube screen to your computer turned out to be the cause of your chronic headaches. You therefore decide to buy one of these new flat TFT monitors. At the entrance of the computer shop you see that it is quite full with customers. In fact, the shop is rather packed with customers and moving in...
30,748
Party Schedule (PARTY) You just received another bill which you cannot pay because you lack the money. Unfortunately, this is not the first time to happen, and now you decide to investigate the cause of your constant monetary shortness. The reason is quite obvious: the lion's share of your money routinely disappears ...
30,749
Dance Floor (DFLOOR) You recently watched a video clip in which a singer danced on a grid of colourful tiles enlightened from below. Each step on a tile flipped the tile's state, i.e. light on or off. In addition to that, all the neighbouring tiles flipped their states, too. In this task, you are supposed to come ...
30,750
Bus (BUS) The city Buscelona (as the name suggests) has a great bus transport system. All buses have circular lines. The bus drivers in Buscelona like to chat. Fortunately most bus lines have some stops in common. If a bus driver meets a colleague on a bus stop they chat a bit and exchange all news they know. The op...
30,751
Tower of Babylon (BABTWR) Apart from the Hanging Gardens the Babylonians (around 3000-539 b.c.) built the Tower of Babylon as well. The tower was meant to reach the sky, but the project failed because of a confusion of language imposed from much higher above. For the 2638th anniversary a model of the tower will be r...
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Fishmonger (FISHER) A fishmonger wants to bring his goods from the port to the market. On his route he has to traverse an area with many tiny city states. Of course he has to pay a toll at each border. Because he is a good business man, he wants to choose the route in such a way that he has to pay as little money fo...
30,753
GX Light Pipeline Inc (LITEPIPE) The GX Light Pipeline Inc. started to prepare bent pipes for the new transgalactic light pipeline. However during the design of the pipeline they ran into the problem of determing how far the light can reach inside the pipe. In order to improve your scarce budget you decided to fill a ...
30,754
Highways (HIGH) In some countries building highways takes a lot of time... Maybe that's because there are many possibilities to construct a network of highways and engineers can't make up their minds which one to choose. Suppose we have a list of cities that can be connected directly. Your task is to count how many wa...
30,755
Alice and Bob (ALICEBOB) This is a puzzle for two persons, let's say Alice and Bob. Alice draws an n-vertex convex polygon and numbers its vertices with integers 1, 2, ... , n in an arbitrary way. Then she draws a number of noncrossing diagonals (the vertices of the polygon are not considered to be crossing p...
30,756
Binary Stirling Numbers (BINSTIRL) The Stirling number of the second kind S(n, m) stands for the number of ways to partition a set of n things into m nonempty subsets. For example, there are seven ways to split a four-element set into two parts: {1, 2, 3} u {4}, {1, 2, 4} u {3}, {1, 3, 4} u {2}, {2, 3, 4} u {...
30,757
Calendar of the Maya (MAYACAL) The Classical Maya civilization developed in what is today southern Mexico, Guatemala, Belize and northern Honduras. During its height they developed a sophisticated system for time keeping which they used both to record history and for divinatory rituals. Their calendar consist...
30,758
Decoding Morse Sequences (MORSE) Before the digital age, the most common "binary" code for radio communication was the Morse code. In Morse code, symbols are encoded as sequences of short and long pulses (called dots and dashes respectively). The following table reproduces the Morse code for the alphabet, where do...
30,759
Exchanges (EXCHNG) Given n integer registers r 1 , r 2 ... r n we define a Compare-Exchange Instruction CE(a, b), where a, b are register indices (1 <= a < b <= n): CE(a, b):: if content(r a ) > content(r b ) then exchange the contents of registers r a and r b ; A Compare-Exchange pr...
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Fill the Cisterns (CISTFILL) During the next century certain regions on earth will experience severe water shortages. The old town of Uqbar has already started to prepare itself for the worst. Recently they created a network of pipes connecting the cisterns that distribute water in each neighbourhood, making it ea...
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Horizontally Visible Segments (SEGVIS) There is a number of disjoint vertical line segments in the plane. We say that two segments are horizontally visible if they can be connected by a horizontal line segment that does not have any common points with other vertical segments. Three different vertical segments...
30,762
Family (FAMILY) We want to find out how much related are the members of a family of monsters. Each monster has the same number of genes but the genes themselves may differ from monster to monster. It would be nice to know how many genes any two given monsters have in common. This is impossible, however, since...
30,763
Intervals (INTERVAL) You are given n closed integer intervals [a i , b i ] and n integers c 1 , ..., c n . Task Write a program that: reads the number of intervals, their endpoints and integers c 1 , ..., c n from the standard input, computes the minimal size of a set Z of integer...
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Rhombs (RHOMBS) An unbounded triangular grid is a plane covered by equilateral triangles: Two neighboring triangles in the grid form a rhomb. There are 3 types of such rhombs: A grid polygon is a simple polygon which sides consist entirely of sides of triangles in the grid. We say that a grid p...
30,765
Servers (SERVERS) The Kingdom of Byteland decided to develop a large computer network of servers offering various services. The network is built of n servers connected by bidirectional wires. Two servers can be directly connected by at most one wire. Each server can be directly connected to at most 10 ...
30,766
Solitaire (SOLIT) Solitaire is a game played on an 8x8 chessboard. The rows and columns of the chessboard are numbered from 1 to 8, from the top to the bottom and from left to right respectively. There are four identical pieces on the board. In one move it is allowed to: move a piece to an ...
30,767
Timetable (TTABLE) You are the owner of a railway system between n cities, numbered by integers from 1 to n. Each train travels from the start station to the end station according to a very specific timetable (always on time), not stopping anywhere between. On each station a departure timetable is available. ...
30,768
Voracious Steve (STEVE) Steve and Digit bought a box containing a number of donuts. In order to divide them between themselves they play a special game that they created. The players alternately take a certain, positive number of donuts from the box, but no more than some fixed integer. Each player's donuts a...
30,769
Paying in Byteland (PAYING) There are infinitely many coin denominations in the Byteland. They have values of 2 i for i=0, 1, 2 ... . We will say that set of coins c1, c2 ... ck is perfect when it is possible to pay every amount of money between 0 and c1 + ... + ck using some of them (so {4, 2, 2, 1} is perfect while...
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Rent your airplane and make money (RENT) "ABEAS Corp." is a very small company that owns a single airplane. The customers of ABEAS Corp are large airline companies which rent the airplane to accommodate occasional overcapacity. Customers send renting orders that consist of a time interval and a price that the cus...
30,771
Square dance (SQDANCE) You are hired by French NSA to break the RSA code used on the Pink Card. The easiest way to do that is to factor the public modulus and you have found the fastest algorithm to do that, except that you have to solve a subproblem that can be modeled in the following way. Let P = {p 1 , p 2 ......
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Help R2-D2! (HELPR2D2) In Episode III of Star Wars (whose alleged title is "How I became Vader"), R2-D2 (Artoo-Detoo) is again confronted to a tedious work. He is responsible for the loading of the republic transport starships in the fastest way. Imagine a huge space area where n starships are parked. Each starship ...
30,773
Phony Primes (PHONY) You are chief debugger for Poorly Guarded Privacy, Inc. One of the top selling product, ReallySecureAgent©, seems to have a problem with its prime number generator. It produces from time to time bogus primes N. After a while, you realize that the problem is due to the way primes are recogniz...
30,774
Men at work (MAWORK) Every morning you have to drive to your workplace. Unfortunately, roads are under constant repair. Fortunately, administration is aware that this may cause trouble and they enforce a strict rule on roadblocks: roads must be blocked only half of the time. However, contractors are free to schedule t...
30,775
Transformation (TRANS) You are given two short sequences of numbers, X and Y. Try to determine the minimum number of steps of transformation required to convert sequence X into sequence Y, or determine that such a conversion is impossible. In every step of transformation of a sequence, you are allowed to replace ...
30,776
Partition (PARTIT) A partition of positive integer m into n components is any sequence a 1 ... a n of positive integers such that a 1 + ... + a n = m and a 1 ≤ a 2 ≤ ... ≤ a n . Your task is to determine the partition, which occupies the k-th position in the lexicographic order of all partitions of m i...
30,777
Election Posters (POSTERS) A parliamentary election was being held in Byteland. Its enterprising and orderly citizens decided to limit the entire election campaign to a single dedicated wall, so as not to ruin the panorama with countless posters and billboards. Every politician was allowed to hang exactly one poster o...
30,778
The Long and Narrow Maze (MAZE) Consider a maze consisting of 3 rows of n square blocks each. The passageways in every block match one of three possible patterns, numbered 0 (empty), 1 (straight) and 2 (bent), as depicted below. Your task is to determine whether it is possible to create a passage in a g...
30,779
The Loner (LONER) The loner is a one-dimensional board game for a single player. The board is composed of squares arranged in a single line, some of which initially have pawns on them. The player makes a move by jumping with a pawn over a pawn on an adjacent field, to an empty square two fields to the right ...
30,780
Johnny and the Glue (GLUE) Little Johnny decided he needed to stick an open metal box to the floor in the hall of his parents' house, so that all guests coming in would trip on it. He knew that as soon as his parents saw what he had done, they would try to remove it, and he wasn't going to stand for this. So,...
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Aliens (ALIENS) Aliens visited our planet with an obvious intention to find some new species for their space zoo. After entering Earth's orbit, they positioned themselves over the town of Belgrade, having detected some life-form activity on the ground. As they approached the surface, they saw a group of half-intellige...
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Fast Multiplication Again (MULTIPLY) After trying to solve Problem Number 31 (Fast Multiplication) with some script languages that support arbitrary large integers and timing out, you wonder what would be the best language to do fast multiplication of integers. And naturally it comes to your mind: Of course it is bra...
30,783
Tautology (TAUT) Write a program that checks if the given logical expression is a tautology. The logical expression is a tautology if it is always true, regardless of logical value of its variables. Input On the first line there is the number of expressions to check (at most 35). The expression is in a prefix ...
30,784
Land for Motorways (MLAND) With every year, the plans for the construction of motorways in Poland are more and more advanced. For some time, it seemed as if the building was actually going to start, so the question of purchasing the land under the roads was of some importance. Only certain cities can be conne...
30,785
Fencing in the Sheep (FSHEEP) A shepherd is having some trouble penning in his flock of sheep. After several hours of ineffectual efforts he gives up, with some of the sheep within their polygon-shaped pen and some outside. Exhausted, he moves to a place within the pen from which he can see the whole interior...
30,786
Where to Drink the Plonk? (PLONK) Consider a city bounded by a square, whose n horizontal and n vertical streets divide it into (n+1) 2 square blocks. However, in tribute to the ancient traditions of the first dwellers (who tended to overindulge in alcohol), all the inhabitants live at crossroads. A group of...
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The Courier (COURIER) Byteland is a scarcely populated country, and residents of different cities seldom communicate with each other. There is no regular postal service and throughout most of the year a one-man courier establishment suffices to transport all freight. However, on Christmas Day there is somewha...
30,788
Balancing the Stone (SCALES) You are given scales for weighing loads. On the left side lies a single stone of known weight W < 2 N . You own a set of N different weights, weighing 1, 2, 4 ... 2 N-1 units of mass respectively. Determine how many possible ways there are of placing some weights on the sides ...
30,789
Sweet and Sour Rock (ROCK) A manufacturer of sweets has started production of a new type of sweet called rock . Rock comes in sticks composed of one-centimetre-long segments, some of which are sweet, and the rest are sour. Before sale, the rock is broken up into smaller pieces by splitting it at the conn...
30,790
Choosing a Palindromic Sequence (PALSEC) Given two sequences of words: X=(x 1 ,...,x n ) and Y=(y 1 ,...,y n ), determine how many binary sequences P=(p 1 ,...,p n ) exist, such that the word concatenation z 1 z 2 ...z n , where z i =x i iff p i =1 and z i =y i iff p i =0, is a palindrome (a word which is the s...
30,791
Paint templates (PAINTTMP) The Painter's Studio is preparing mass production of paintings. Paintings are going to be made with aid of square matrices of various sizes. A matrix of size i consists of 2 i rows and 2 i columns. There are holes on intersections of some rows and columns. Matrix of size 0 has one hole. ...
30,792
Polygon (POLY1) We say that two triangles intersect if their interiors have at least one common point. A polygon is called convex if every segment connecting any two of its points is contained in this polygon. A triangle whose vertices are also vertices of a convex polygon is called an elementary triangle of this poly...
30,793
Sum of one-sequence (SUM1SEQ) We say that a sequence of integers is a one-sequence if the difference between any two consecutive numbers in this sequence is 1 or -1 and its first element is 0. More precisely: [ a 1 , a 2 , ..., a n ] is a one-sequence if for any k , such that 1 <= k < n : | a k - a k +1...
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AB-words (ABWORDS) Every sequence of small letters a and b (also the empty sequence) is called an ab-word. If X = [ x 1 ... x n ] is an ab-word and i , j are integers such that 1 ≤ i ≤ j ≤ n then X [ i .. j ] denotes the subword of X consisting of the letters x i ... x j . We say that an ab-word X ...
30,795
Road net (ROADNET) A diskette was enclosed to a road map. The diskette contains the table of the shortest ways (distances) between each pair of towns on the map. All the roads are two-way. The location of towns on the map has the following interesting property: if the length of the shortest way from town A to town B ...
30,796
Word equations (WORDEQ) Every non-empty sequence of elements 0 and 1 is called a binary word. A word equation is an equation of the form x 1 x 2 ... x l = y 1 y 2 ... y r , where x i and y j are binary digits (0 or 1) or variables i.e. small letters of English alphabet. For every variable there is a fixed lengt...
30,797
How to pack containers (CONTPACK) Products of a factory are packed into cylindrical boxes. All boxes have the same bases. A height of a box is a non-negative integer being a power of 2, i.e. it is equal to 2 i for some i = 0, 1, 2, ... . The number i (exponent) is called a size of a box. All boxes contain the sam...
30,798
Scuba diver (SCUBADIV) A scuba diver uses a special equipment for diving. He has a cylinder with two containers: one with oxygen and the other with nitrogen. Depending on the time he wants to stay under water and the depth of diving the scuba diver needs various amount of oxygen and nitrogen. The scuba diver has at hi...
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