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Milking Cows Three farmers riseat 5 am each morning and head for the barn to milk three cows. The first farmerbegins milking his cow at time 300 (measured in seconds after 5 am) and ends attime 1000.

Consider the set of all reduced fractions between 0 and 1 inclusive with denominators less than or equal to N. Here is the set when N = 5: 0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1/1 Write a progr

A 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 the standard set:

Sorting is one of the most frequently performed computational tasks. Consider the special sorting problem in which the records to be sorted have at mostthree different key values. This happens for ins

Farmer John prides himself on having the healthiest dairy cows in the world. He knows the vitamin content for one scoop of each feed type and the minimum daily vitamin requirement for the cows. Help F

Given N, B, and D: Find a set of N codewords (1 <= N <= 64), each of length B bits (1 <= B <= 8), such that each of the codewords is at least Hamming distance of D (1 <= D <= 7) away from each of the

Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be passed on a route that starts at the top and ends somewhere on the base. Each step can

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

Farmer 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 while bucket C is

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

Among the large Wisconsin cattle ranchers, it is customary to brand cows with serial numbers to please the Accounting Department. The cow hands don't appreciate the advantage of this filing system, th

Barn Repair It was a dark and stormy night that ripped the roof and gates off the stalls that hold Farmer John's cows. Happily, many of the cows were on vacation, so the barn was not completely ful

An 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. Write a program that finds

Butchering 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 John ensures that

Examine 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 than one in any diag

In 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 only the winning number for th

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

Palindromes are numbers that read the same forwards as backwards. The number 12321 is a typical palindrome. Given a number base B (2 <= B <= 20 base 10), print all the integers N (1 <= N <= 300 bas

For 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 so that the sums of both subsets are identical: {3} and {1,2} This