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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...
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- Fall '10
- Computer Science