This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 6.042/18.062J Mathematics for Computer Science September 17, 2010 Tom Leighton, Marten van Dijk Problems for Recitation 3 1 Problem: Breaking a chocolate bar We are given a chocolate bar with m n squares of chocolate, and our task is to divide it into mn individual squares. We are only allowed to split one piece of chocolate at a time using a vertical or a horizontal break. For example, suppose that the chocolate bar is 2 2. The first split makes two pieces, both 2 1. Each of these pieces requires one more split to form single squares. This gives a total of three splits. Prove that the number of times you split the bar does not depend on the sequence of splits you make. Recitation 3 2 2 Problem: The Temple of Forever Each monk entering the Temple of Forever is given a bowl with 15 red beads and 12 green beads. Each time the Gong of Time rings, a monk must do one of two things: 1. Exchange : If he has at least 3 red beads in his bowl, then he may exchange 3 red beads for 2 green...
View Full Document
- Fall '10
- Computer Science