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Power Eggs Description: Benedict bought $K$ identical power eggs from Dropeggs.com, and now he wants to test them by dropping them from different floors of his building. His building has $N$ floors numbered $1$ to $N$. $F$ is an unknown number in the range from $0$ to $N$, inclusive. Each egg will brea...
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Power Grid Description: A city consists of a rectangular $N \times M$ grid of blocks. Each block $(i, j)$ has some unknown power consumption $A_{i, j}$. Some of the city blocks house power stations, while some might have no buildings in them at all, so it’s possible that $A_{i, j}$ is positive,...
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Power Signs Description: You are probably familiar with the binary representation of integers, i.e. writing a nonnegative integer $n$ as $\sum _{i=0}^ k a_ i \cdot 2^ i$, where each $a_ i$ is either $0$ or $1$. In this problem, we consider a so called signed binary representation, in which we still ...
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Power String Matching Description: For two strings $s_1$ and $s_2$, let $s_1 + s_2$ denote their concatenation, e.g. abc + cda is the string abccda. Now for a string $s$ and an integer $k \geq 0$ we let $s^ k$ denote the result of concatenating $k$ copies of $s$, i.e. $\texttt{ab}^3 = \texttt{...
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Power Strings Description: Given two strings $a$ and $b$ we define $a\cdot b$ to be their concatenation. For example, if $a = \text {"abc"}$ and $b = \text {"def"}$ then $a\cdot b = \text {"abcdef"}$. If we think of concatenation as multiplication, exponentiation by a non-negative integer i...
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Power of Divisors Description: Consider a positive integer $n$. Let $f(n)$ be the number of positive integer divisors of $n$. For example, if $n=8$ then $f(n)=4$, since the divisors of $8$ are $1$, $2$, $4$ and $8$. Now, consider a positive integer $x$. What is the smallest value of $n$ such t...
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Powers and Modulus Description: One day you and GTmac walk into a classroom and see a mysterious expression on the blackboard: Upon seeing the expression GTmac shows an evil smile and challenges you: “Let me give you the values of $a$ and $b$ and let’s assume $b$ is an odd number. Want to bet who can eval...
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Powers of 2 Description: Theta has been learning about powers of $2$ in school. She notices that some numbers when written out contain powers of $2$ in their digit representation: for instance, $12\, 560$ contains $256$ which is a power of $2$. She has been wondering how many such numbers there are...
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Powers of 2 (Easy) Description: Theta has been learning about powers of $2$ in school. She notices that some numbers when written out contain powers of $2$ in their digit representation: for instance, $12\, 560$ contains $256$ which is a power of $2$. She has been wondering how many such numbers th...
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Pravokutni Description: $N$ points are placed in the coordinate plane. Write a program which calculates in how many ways a right triangle can be formed by three of the given points. A right triangle is one in which one of the angles is $90$ degrees. ## Input The first line of input contains an integer $...
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Precarious Stacks Description: It’s been difficult finding a job in the tech industry lately. You managed to land a job working for a construction company, but some of the tasks being assigned to you have you wondering whether the engineers have ever heard of gravity. Anyway, in the latest task, you ar...
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Predicting GME Description: GME is the stock market ticker symbol for Gamestop, which is famously known around the world today for its short squeeze phenomenon. This incident caused major financial consequences for rich hedge funds, and brought money to many young, naive investors. Sarah recently beca...
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Prefix Free Code Description: Consider $n$ initial strings of lower case letters, where no initial string is a prefix of any other initial string. Now, consider choosing $k$ of the strings (no string more than once), and concatenating them together. You can make this many such composite strings: C...
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Prehistoric Programs Description: Taken together, the tablets appear to describe a great piece of work – perhaps a program, or an epic, or even tax records! Unsurprisingly, after such a long time, the tablets are in a state of disorder. Your job is to arrange them into a sequence so that the resulting ...
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Preludes Description: Frederic Chopin was a Polish music composer who lived from 1810–1849. One of his most famous works was his set of preludes. These $24$ pieces span the $24$ musical keys (there are musically distinct $12$ scale notes, and each may use major or minor tonality). The $12$ distinct...
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Prerequisites? Description: Freddie the frosh has chosen to take $k$ courses. To meet the degree requirements, he must take courses from each of several categories. Can you assure Freddie that he will graduate, based on his course selection? ## Input Input consists of several test cases, at most $50$. Fo...
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Presidential Elections Description: 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 tha...
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Pretty Good Cube Root Description: Given a positive integer $x$, the cube root of $x$ may or may not be an integer. We’ll define an approximate cube root of $x$ as the positive integer $y$ such that $y^3$ is as close is possible to $x$. ## Input Input has up to $100$ lines with one positive integer p...
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Primal Partitions Description: The Math department has challenged the Computer Science department at your University to solve a difficult puzzle in Discrete Mathematics. With the pride of your Computer Science department at stake, you must solve this puzzle! In this puzzle, you are given a sequence of $n$...
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Primal Representation Description: The fundamental theorem of arithmetic says that every integer can be represented as a unique product of prime numbers. For example, consider the number $319\, 176$. It can be written as the product $31 \times 3 \times 3 \times 2 \times 2 \times 2 \times 13 \times 11$,...
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Primality Description: Given a positive integer $N$, determine whether it is prime or not. ## Input The first line contains the integer $N$ ($2 \le N \le 10^{18}$). ## Output Output YES if $N$ is prime, and NO otherwise. ## Scoring Your solution will be tested on a set of test groups, each worth a nu...
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Primary Arithmetic Description: Children are taught to add multi-digit numbers from right-to-left one digit at a time. Many find the “carry” operation – in which a $1$ is carried from one digit position to be added to the next – to be a significant challenge. Your job is to count the number of carr...
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Primary Register Description: The only operation available is an “increment” operation. When it is performed, the size $2$ register is increased by $1$. If this increment causes overflow (i.e., if the old value was $1$) the value is reset to $0$, and the size $3$ is incremented. If this causes ...
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Primary X-Subfactor Series Description: Let $n$ be any positive integer. A factor of $n$ is any number that divides evenly into $n$, without leaving a remainder. For example, $13$ is a factor of $52$, since $52/13 = 4$. A subsequence of $n$ is a number without a leading zero that can be obtained fr...
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Prime Bitcount Description: This problem is very easy to describe. In fact, it is so easy to describe that there is really no need for a preamble such as the one you are reading right now, which makes it surprising that the problem author didn’t just omit this part and skip directly to the Input and Ou...
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Prime Count Description: Given a positive integer $N$, compute the number of primes less than $N$. ## Input The first line contains the integer $N$ ($1 \le N \le 10^{11}$). ## Output Print the number of primes less than or equal to $N$. ## Scoring Your solution will be tested on a set of test groups,...
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Prime Matrix Description: A Prime Matrix is defined as an $n \times n$ square matrix satisfying: * All numbers in the matrix are positive integers, and * The numbers in each row are distinct, and * The numbers in each column are distinct, and * The sum of numbers in each row is a prime number, and ...
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Prime Path Description: Now, the minister of finance, who had been eavesdropping, intervened. — No unnecessary expenditure, please! I happen to know that the price of a digit is one pound. — Hmm, in that case I need a computer program to minimize the cost. You don’t know some very cheap software gu...
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Prime Reduction Description: A prime number $p \geq 2$ is an integer which is evenly divisible by only two integers: 1 and $p$. A composite integer is one which is not prime. The fundamental theorem of arithmetic says that any integer $x$ can be expressed uniquely as a set of prime factors – those ...
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Prime Sieve Description: ## Input The first line of input consists of two integers $n$, $q$, where $1 \leq n \leq 10^8$ and $1 \leq q \leq 20000$. Then follow $q$ lines, each containing an integer $x$ satisfying $1 \leq x \leq n$. ## Output On the first line of output, write one line giving the ...
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Prime Spiral Description: Boredom can be good for creativity. Polish mathematician Stanislaw Ulam (1909-1984) discovered the eponymous Ulam spiral while listening to a “long and very boring paper”. He started by writing down the positive integers in a spiral on a grid, one number per grid cell. Then he...
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Prime Time Description: 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,...
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Primitive Roots Description: Primitive roots modulo $m$ are values $g$ such that $g^{\phi (m)} = 1 \pmod{m}$ but $g^k \neq 1 \pmod{m}$ for all $k < \phi (m)$. Such values only exist if $m = 1, 2, 4, p^k$ or $2p^k$ where $p$ is an odd prime and $k \geq 1$. Find such a value $g$ for $m$ or report that ...
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Primonimo Description: Primonimo is a game played on an $n \times m$ board filled with numbers taken from the range $1 \ldots p$ for some prime number $p$. At each move, a player selects a square and adds $1$ to the numbers in all squares in the same row and column as the selected square. If a squa...
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Prince and Princess Description: On an $n \times n$ chessboard, the Prince and the Princess play a game. The squares on the chessboard are numbered $1, 2, 3, \ldots , n^2$, as shown in Figure 1: The Prince stands in square $1$, makes $p$ jumps and finally reaches square $n^2$. He enters a square a...
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Princeza Description: Luka parked his truck near the lake. The lake is inhabited by the frog Barica, who jumps acrossplants floating on the lake’s surface. Knowing a fair number of folk tales, Luka knows that if he kisses Barica, she will turn into a beautiful princess. However, he needs to catch her f...
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Prinova Description: Brojko and Brojana are happily married with $N$ little boys. The boys are named with distinct even integers $P_1, P_2, \ldots , P_ N$. Brojko and Brojana are expecting an addition to their family and have to come up with a nice name for the little girl. They have decided that the ...
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PrintQuoter3D Description: With the commoditization of 3D printing, Mat Hedicine decided to try his hand at starting his own 3D printing business. He knows there is a lot of competition in this space and he needs a way to distinguish himself. Knowing that few people are good at CAD, he thought, what if...
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Printer Scheduling Description: There are $n$ files to be printed using $m$ identical printers. The files are numbered from $1$ to $n$. The printers are numbered from $1$ to $m$. Assuming each page takes one unit of time to print, for each file $i$, we have the following information: * The number ...
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Printing Costs Description: Your workplace is starting to become concerned with the cost of toner used for printing. Of course, some pages are more expensive to print than others. Your job is to write a program that helps to figure out how much toner it will take. Each character requires a different amoun...
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Pripreme Description: Ante and Goran are preparing $N$ teams of young ambitious students for a student programming competition of students from University of Zagreb. Both of them have one algorithm they have to explain to each team. Of course, both can’t work with the same team at the same time and non...
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Prison Rearrangement Description: In order to lower the risk of riots and escape attempts, the boards of two nearby prisons of equal prisoner capacity, have decided to rearrange their prisoners among themselves. They want to exchange half of the prisoners of one prison, for half of the prisoners of the...
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Private Space Description: 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...
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Prjónamynstur Description: Heiðrún thoroughly enjoys knitting all sorts of garments for her family members. Whenever a new baby arrives in the family, one can expect that a dress, hat or sweater is her next project. When Heiðrún knits, she often makes use of recipes, also known as knitting patterns, w...
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Probe Droids Description: After being stationed on Hoth, you’ve decided that this is the worst decision you have ever made. The planet is cold, there is nothing to do, and to make matters worse, the Empire keeps sending probe droids down to see if anyone is hiding on the planet. At least you can do som...
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Problem Classification Description: When reading programming problems, one can often get some hints regarding the topic of the problem by skimming the problem statement for certain words. If, for example, the word “vertex” or “edge” appears, the problem is almost certainly a graph problem, while the wo...
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Problem Set Construction Description: You are a judge, constructing a problem set for a contest. You have a pool of candidate problems. For each problem, you’ve found the probability that a team is able to solve the problem, and the time it will take them to implement the solution if they are able to s...
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Problematic Polygons Description: You are an employee at the Polygon Packing Plant, where your job is to pack objects with simple polygon shapes into containers with simple polygon shapes. However, the object and containers are often misaligned, so the object may need to be rotated before it can fit in...
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Product Digit Description: 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 $...
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Product Divisors Description: Given a sequence of integers $a_1, a_2, \dots a_ n$, compute the number of divisors of their product $A = \prod _{i=1}^ n a_ i$. ## Input The first line contains the number of integers in the sequence $n$ ($1 \le n \le 10^6$). The second line contains the $n$ space-separated in...
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Prof. Fumblemore and the Collatz Conjecture Description: The Collatz function, C(n), on positive integers is: The Collatz sequence, CS(n), of a positive integer, n, is the sequence For example, CS(12) = 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, … The Collatz Conjecture (also known as the 3n+1 pr...
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Profitable Pizzas Description: A new app available in Calgary allows people to sign-up to deliver pizzas in exchange for money. Every first of the month, a new list of pizzas to deliver is available. Each entry on the list contains the amount of money the delivery-person will earn to deliver the pizza,...
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Profitable Trip Description: You are planning a road trip. You have carefully mapped out all potential waypoints that you may stop at. From each waypoint, there are roads that allow you to drive to other waypoints, but roads can only be used in one direction. In order to alleviate traffic jams, the roa...
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Program Description: Mirko is trying to debug a piece of his code. First he creates an array of $N$ integers and fills it with zeros. Then he repeatedly calls the following C++ procedure: ``` void something( int jump ) { int i = 0; while( i < N ) { seq[i] = seq[i] + 1; i = i + jump; } } ``` ...
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Programmeringsolympiaden's Budget Description: Programmeringsolympiaden (PO) must write a budget every year, which then needs to be approved by the treasurer Emil. This year, the PO leadership has proposed some rather wild ideas, such as buying 2000 ducks and purchasing a PO-yacht to sail to the IOI (t...
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Programming Team Description: UpCoder is looking to assign their best employees to a team tasked with designing their new and improved website, and they’re looking to you to help them form the team. There are $n$ potential candidates. The CEO is employee number $0$, and the candidates are all assig...
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Programming Team Selection Description: You are a coach for a competitive learning program. It’s time for the regional competition and you have to group your students into teams. Every team needs exactly three members and every student needs to be on a team. While choosing your teams, you must keep in min...
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Programming Tutors Description: You are the founder of the Bruce Arden Programming Collective, which is a tutoring programme that matches experienced programmers with newbies to teach them. You have $N$ students and $N$ tutors, but now you have to match them up. Since the students will have to trav...
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Progressive Scramble Description: You are a member of a naive spy agency. For secure communication, members of the agency use a very simple encryption algorithm – which changes each symbol in the message ‘progressively’, i.e., based on the symbols preceding it. The allowed symbols are space and the $26...
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Prokletnik Description: 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 integer...
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Prolonged Password Description: Kang the Penguin has forgotten some letters of his password, help him figure them out! Of course, Kang knows that something as important as a password should be easy to remember, but it also cannot be too short. Thus, he knows that he originally decided to generate his ...
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Promotions Description: The Fair Inc. administration decided to promote the best employees and limited the number of promotions to a fixed interval $[A,B]$. The directors compared the employees’ performance and their evaluations resulted in a consistent precedence relation among employees, which ha...
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Proofs Description: You are teaching discrete math. You have done your best to teach your students about axioms and inference rules, proofs and theorems. Sometimes the students write beautiful proofs that Fermat would be proud of but sometimes, also like Fermat, their proofs are not quite right. You ar...
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Prosjek Description: 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...
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Prosjek Description: You are given an array of $N$ integers. Find a consecutive subsequence of numbers of the length at least $K$ that has the maximal possible average. ## Input The first line of input contains two integers $N$ ($1 \leq N \leq 3 \cdot 10^5$) and $K$ ($1 \leq K \leq N$). The second li...
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Prospecting Description: Prospectin’ Pete has a lead on a new titanium mine, and needs your help pitching a mining operation to investors. The mine can be represented as a tree: the mine entrance is the root of the tree, other tree nodes are pockets of underground titanium ore, and the tree edges are p...
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Prosti Description: 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 $1, 2, \ldots , K$)...
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Protect the Pollen! Description: The Flariana flowers and the bumblebees form one of the nicest partnerships in the rainforest. In spring, several flowers bloom and start producing pollen. Special vines form a network of bridges between the flowers. Using the vines, there is exactly one way to get from...
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Protecting the Collection Description: Nathaniel collects rare gems and minerals, and has decided he has to protect his valuable collection from thieves. He is installing an electric eye system, in which he shines a laser into the room with his collection, and the laser will hit a sensor as long as no ...
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Protein Synthesis Description: Latbo is well known to be the laziest city in Sweden. Björn has had the goal of being the laziest in town since he was little. Yesterday, he made it all the way to the final in this year’s laziness competition. He was fully prepared to win but was completely crushed when ...
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Proteins Description: Magnus is a biologist. He is playing with proteins all day long and now he wants to know what these molecules look like. He has heard that X-ray crystallography can be used to get images of proteins that contain a lot of sulfur atoms. Magnus does not think his proteins contain eno...
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Provinces and Gold Description: Jake is learning how to play the card game Dominion. In Dominion, you can buy a variety of treasure, action, and victory point cards – at the end of the game, the player with the most victory points wins! Each turn, each player draws $5$ cards and can use their action and ...
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Proving Equivalences Description: Consider the following exercise, found in a generic linear algebra textbook. * $A$ is invertible. * $Ax = b$ has exactly one solution for every $n \times 1$ matrix $b$. * $Ax = b$ is consistent for every $n \times 1$ matrix $b$. * $Ax = ...
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Prozor Description: Young Marin, now already a respectable star of Croatian cinematography, spends his free time looking out the window. Unfortunately for him, the same activity is also taken up by a few flies that have landed on his window and are looking into the distance. Marin immediately hurried t...
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Prsteni Description: After an exhausting morning, Mirko fell asleep. His brother Stanko, however, just awoke and, like his brother, is all about excitement. Stanko found N rings of varying radii in the garage. He arranged them on the floor so that each ring (except the first and last) touches the ones ...
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Prva Description: Little Ivica solves crossword puzzles every day. In case you haven’t seen one, a crossword puzzle starts on a grid of $R \times C$ squares, each of which is either empty or blocked. The player’s task is to write words in consecutive empty squares vertically (top down) or horizonta...
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Pseudo-random Numbers Description: Access to high-quality randomness is very important for many applications, especially in cryptography. Radioactive decay is sometimes used as a source of “true randomness”, but this is a fairly slow procedure for getting random numbers. Also, in many applications it i...
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Pseudoprime numbers Description: Fermat’s theorem states that for any prime number $p$ and for any integer $a \ge 0$, $a^ p \equiv a \pmod{p}$. That is, if we raise $a$ to the $p$th power and divide by $p$, the remainder is $a$. Some (but not very many) non-prime values of $p$, known as bas...
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Ptice Description: Adrian, Bruno and Goran wanted to join the bird lovers’ club. However, they did not know that all applicants must pass an entrance exam. The exam consists of $N$ questions, each with three possible answers: A, B and C. Unfortunately, they couldn’t tell a bird from a whale so they ar...
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Pub Crawl Description: Fritjof is going to his first ever pub crawl. Since he doesn’t want to go all out on his very first time, he’s decided that he’s only going to visit a single pub. As he likes all pubs equally much he will stay at the pub for an equal amount of time regardless of which pub it is. ...
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Pub-lic Good Description: A bit over three years ago, you were elected president of the glorious and picturesque country of Molvanîa, a land untouched by modern dentistry. To secure your landslide victory in the election you had to make a few promises, some of which, with the clarity of hindsight, may ...
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Pulling Their Weight Description: To save money, Santa Claus has started hiring other animals besides reindeer to pull his sleigh via short term ‘gig’ contracts. As a result, the actual animals that show up to pull his sleigh for any given trip can vary greatly in size. Last week he had $2$ buffalo, $...
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Pulverizing Pancake Description: You were walking along minding your own business when you were suddenly ambushed by a horde of wild Pokemon. The world is a grid with $N$ columns numbered from $1$ to $N$, and each Pokemon is in one of the columns hoping to trap you, but you have come prepared. ...
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Pumpkin Patch Description: Pumpkin Pete is trying out a new type of “rapid-growth” pumpkin seed that he bought from the farmer’s market. Without looking at the directions, Pumpkin Pete tears through the packaging and plants the seeds he has into his pumpkin patch. Unbeknownst to Pumpkin Pete, his rival...
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Purple Rain Description: On close observation however, Prof. Nelson Rogers finds that actually it is a mix of Red and Blue drops. In his zeal, he records the location and color of the raindrops in different locations along the peninsula. Looking at the data, Professor Rogers wants to know which part of ...
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Putnik Description: 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 ...
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Putovanje Description: Young Mislav loves spending time in nature and, most of all, he loves spending time in forests. The fresh air and lovely sounds make the forest his favourite location. Mislav has decided to spend this afternoon in a forest and, because he’s so practical, he’s also decided to stuf...
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Puzzle Description: Sam loves all kinds of puzzles. Recently he received a very special puzzle – a grid of $N \times M$ squares, each square is occupied either by a red or by a blue pebble. The puzzle is controlled by several buttons. Each row of the grid has its corresponding black button. When y...
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Pyramid Construction Description: Kim likes building Lego pyramids and now wants to build one of height $H$. How many more bricks are needed if Kim already has $N$ bricks of size $2 \times 2$ and $M$ bricks of size $4 \times 2$? A pyramid is hollow and consists of $H$ layers, as shown in the image. The...
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Pyro Tubes Description: The Impressively Calculable Pyrotechnics Company has been contracted to provide certain stage effects for a rock festival. In particular, fire is requested (because fire makes the crowd go wild). In order to pull this off, the main stage is outfitted with a series of tubes, each...
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Pönnukökur Description: Signý is making pancakes. The pancakes have two sides, side $0$ and side $1$, and they have been arranged into a row. Thus what side faces up can be denoted by binary. Initially side $0$ faces up. Sometimes when she’s cooking the pancakes she flips them. If she flips a panca...
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Púsluspil Description: Davíð really enjoys jigsaw puzzles, so much so that he recently bought one from Baldi’s Puzzle Shop. He eagerly goes home and starts working on the puzzle. When he’s almost done, Davíð realises that there are some puzzle pieces missing in the almost completed puzzle, but the box ...
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Pýramídasala Description: The company Pyramids Inc. sells hundreds of pyramids each year. Their business model is different from what is commonly known in companies. Pýramídas, the owner, hired employees to sell for the company. His employees then hired their own employees, which in turn hired their ow...
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QC QC Description: Innovative Computable Quality Control (ICQC) has developed a ground-breaking new machine for performing, well, quality control. Thanks to its novel Deep Intelligence technology, an ICQC quality control (QC) machine can automatically, with $100\% $ accuracy, detect manufacturing e...
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Qanat Description: A qanat is an irrigation system widely used to deliver water in hot, arid climates. The technology was originally developed by Persians over 2000 years ago. In Morocco, qanats are known as khettara and are still used today in the southern part of the country. The basic feature of a ...
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Quadrant Selection Description: A common problem in mathematics is to determine which quadrant a given point lies in. There are four quadrants, numbered from $1$ to $4$, as shown in the diagram below: For example, the point $A$, which is at coordinates $(12, 5)$ lies in quadrant $1$ since both...
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Quadratic Dissonance Description: Oh no! Both you and your lab partner forgot to complete one part of the latest assignment and it is due in an hour! The purpose of this lab assignment was to have you analyze some experimental data, find a quadratic function that best describes the data, and report the mi...
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Quadratic Residues Description: The great German mathematician C. F. Gauss studied the criteria for the equation to have an integer solution $x$ for a prime $p$. For some tuples $a$ and $p$ there are several solutions, whereas others have none. For instance, $x^2\equiv 2 \pmod{7}$ has the solutions $3+7k$...
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Qualification Round Description: You’ve just advanced from the Qualification Round of Google Code Jam Africa 2010, and you want to know how many of your fellow contestants advanced with you. To give yourself a challenge, you’ve decided only to look at how many people solved each problem. The Qualifica...
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Quality-Adjusted Life-Year Description: The Quality-Adjusted Life-Year (QALY) is a way to measure a person’s quality of life that includes both the quality and the quantity of life lived. The quality of life lived can be quantified as a number between $0$ and $1$. If someone is living with perfect...
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