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DescriptionIf a and d are relatively prime positive integers, the arithmetic sequence beginning witha and increasing by d, i.e., a, a + d,a + 2d, a + 3d, a + 4d, ..., contains infinitely many

DescriptionIn 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d s

DescriptionAs part of an arithmetic competency program, your students will be given randomly generated lists of from 2 to 15 unique positive integers and asked to determine how many items in each li

DescriptionProblems in Computer Science are often classified as belonging to a certain class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will be analyzing a property of an alg

DescriptionThe king pays his loyal knight in gold coins. On the first day of his service, the knight receives one gold coin. On each of the next two days (the second and third days of service), the

DescriptionA certain prison contains a long hall of n cells, each right next to each other. Each cell has a prisoner in it, and each cell is locked.One night, the jailer gets bored and decides to

DescriptionBill and Ted are taking a road trip. But the odometer in their car is broken, so they don't know how many miles they have driven. Fortunately, Bill has a working stopwatch, so they can re

DescriptionHow far can you make a stack of cards overhang a table? If you have one card, you can create a maximum overhang of half a card length. (We're assuming that the cards must be perpendicul

DescriptionIn how many ways can you tile a 2xn rectangle by 2x1 or 2x2 tiles?Here is a sample tiling of a 2x17 rectangle. InputInput is a sequence of lines, each line containing an int

DescriptionFarmer John wants to repair a small length of the fence around the pasture. He measures the fence and finds that he needsN (1 ≤ N ≤ 20,000) planks of wood, each having some integer le

DescriptionAccounting for Computer Machinists (ACM) has sufferred from the Y2K bug and lost some vital data for preparing annual report for MS Inc.All what they remember is that MS Inc. posted a

DescriptionCurrent work in cryptography involves (among other things) large prime numbers and computing powers of numbers among these primes. Work in this area has resulted in the practical use of r

DescriptionFred Mapper is considering purchasing some land in Louisiana to build his house on. In the process of investigating the land, he learned that the state of Louisiana is actually shrinking

DescriptionBackgroundBinary trees are a common data structure in computer science. In this problem we will look at an infinite binary tree where the nodes contain a pair of integers. The tree is c

DescriptionSuppose you are reading byte streams from any device, representing IP addresses. Your task is to convert a 32 characters long sequence of '1s' and '0s' (bits) to a dotted decimal format.