Broken Necklace You have a necklace of N red, white, or blue beads (3 1 2 1 2 r b b r b r r b r

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

Mother's Milk 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

Superprime Rib Butchering Farmer John's cows always yields the best prime rib. Youcan tell prime ribs by looking at the digits lovingly stamped acrossthem, one by one, by FJ and the USDA. Farmer

The Castle IOI'94 - Day 1 In a stroke of luck almost beyond imagination, Farmer John wassent a ticket to the Irish Sweepstakes (really a lottery) for hisbirthday. This ticket turned out to have on

Ordered Fractions Consider the set of all reduced fractions between 0 and 1 inclusivewith 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

Sorting a Three-Valued Sequence IOI'96 - Day 2 Sorting is one of the most frequently performed computational tasks.Consider the special sorting problem in which the records to be sortedhave at

Healthy Holsteins Burch & Kolstad Farmer 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 vita

Hamming Codes Rob Kolstad 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 codewordsis at least Hamming distance of D (1 <= D

Preface Numbering 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

Subset Sums JRM 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: {

Runaround Numbers Runaround numbers are integers with unique digits, none of which is zero (e.g., 81362) that also have an interesting property, exemplified by this demonstration: If you start

Longest Prefix IOI'96 The structure of some biological objects is represented by the sequence of their constituents, where each part is denote by an uppercase letter. Biologists are interested in

Number Triangles Consider the number triangle shown below. Write a program thatcalculates the highest sum of numbers that can be passed on a route thatstarts at the top and ends somewhere on the

Milking Cows Three farmers rise at 5 am each morning and head for the barnto milk three cows. The first farmer begins milking his cow at time 300 (measured in seconds after 5 am) and ends at time 1

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

Calf Flac It is said that if you give an infinite number of cows an infinitenumber of heavy-duty laptops (with very large keys), that they willultimately produce all the world's great palindromes

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

Name That Number Among the large Wisconsin cattle ranchers, it is customary to brandcows with serial numbers to please the Accounting Department. The cowhands don't appreciate the advantage of th

Palindromic Squares Rob Kolstad 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

Dual Palindromes Mario Cruz (Colombia) & Hugo Rickeboer (Argentina) A number that reads the same from right to left as when read fromleft to right is called a palindrome. The number 12321 is a pal

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

Arithmetic Progressions 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 anon-negative integer and b is a positive integer.

Transformations A square pattern of size N x N (1 <= N <= 10) black and whitesquare tiles is transformed into another square pattern. Write a programthat will recognize the minimum transformation

Mixing Milk Since milk packaging is such a low margin business, it is importantto keep the price of the raw product (milk) as low as possible. HelpMerry Milk Makers get the milk they need in the

Prime Cryptarithm The following cryptarithm is a multiplication problem that can besolved by substituting digits from a specified set of N digits into thepositions marked with *. If the set of pr

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

Your Ride Is Here It is a well-known fact that behind every good comet is a UFO. TheseUFOs often come to collect loyal supporters from here on Earth.Unfortunately, they only have room to pick up on

Checker Challenge Examine the 6x6 checkerboard below and note that the six checkersare arranged on the board so that one and only one is placed in eachrow and each column, and there is never more