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Greedy Gift GiversA group of NP (2 ≤ NP ≤ 10) uniquely named friends has decided to exchange gifts of money. Each of these friends might or might not give some money to any or all of the other fri

Friday the ThirteenthIs Friday the 13th really an unusual event?That is, does the 13th of the month land on a Friday less often than on any other day of the week? To answer this question, wr

Preface NumberingA certain book's prefaces are numbered in upper case Roman numerals. Traditional Roman numeral values use a single letter to represent a certain subset of decimal numbers. Here is

WormholesFarmer John's hobby of conducting high-energy physics experiments on weekends has backfired, causing N wormholes (2 <= N <= 12, N even) to materialize on his farm, each located at a disti

The CastleIOI'94 - Day 1In a stroke of luck almost beyond imagination, Farmer John was sent a ticket to the Irish Sweepstakes (really a lottery) for his birthday. This ticket turned out to have on

Subset SumsJRMFor many sets of consecutive integers from 1 through N (1 For example, if N=3, one can partition the set {1, 2, 3} in one way sothat the sums of both subsets are identical:{3}

Healthy HolsteinsBurch & KolstadFarmer John prides himself on having the healthiest dairy cowsin the world. He knows the vitamin content for one scoop of eachfeed type and the minimum daily vitami

Superprime RibButchering Farmer John's cows always yields the best prime rib. You can tell prime ribs by looking at the digits lovingly stamped across them, one by one, by FJ and the USDA. Farmer

Prime PalindromesThe number 151 is a prime palindrome because it is both a prime number and a palindrome (it is the same number when read forward as backward). Write a program that finds all prime

Arithmetic ProgressionsAn arithmetic progression is a sequence of the form a, a+b, a+2b, ..., a+nb where n=0,1,2,3,... . For this problem, a is a non-negative integer and b is a positive integer.

Checker ChallengeExamine the 6x6 checkerboard below and note that the six checkers are arranged on the board so that one and only one is placed in each row and each column, and there is never more

Mother's MilkFarmer John has three milking buckets of capacity A, B, and C liters. Each of the numbers A, B, and C is an integer from 1 through 20, inclusive. Initially, buckets A and B are empty

Packing RectanglesIOI 95 The six basic layouts of four rectanglesFour rectangles are given. Find the smallest enclosing (new) rectangle into which these four may be fitted without overlapping.

The ClocksIOI'94 - Day 2Consider nine clocks arranged in a 3x3 array thusly:|-------| |-------| |-------| | | | | | | | |---O | |---O | | O |

Calf FlacTime Limit: 1000 ms   Case Time Limit: 1000 ms   Memory Limit: 64 MBJudge By CaseDescriptionIt is said that if you give an infinite number of cows an infinite number ofheavy-dut

Combination LockFarmer John's cows keep escaping from his farm and causing mischief. To try and prevent them from leaving, he purchases a fancy combination lock to keep his cows from opening the