The Wednesday Morning Math Challenge: Week 5

Welcome to Week 5 of the Wednesday Morning Math Challenge. You can find solutions to the Week 4 puzzles here, along with — more importantly — discussions of some ways to approach them. Remember that the real goal here is to think creatively.

This week I have three puzzles from my favorite puzzle book, The Moscow Puzzles. Translated from Russian, this is the most popular puzzle book ever published in the Soviet Union. You can check out the book here.

Here are three puzzles from the book, involving checkers.

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1. Jumping Checkers

Place 3 white checkers in squares 1, 2, and 3 of the figure, and 3 black ones on the squares 5, 6, and 7. Shift the white checkers to the squares occupied by the black ones, and vice versa. You may move a checker forward to the adjacent unoccupied square, if any. You may jump a checker forward over an adjacent checker into the vacant square. The solution requires 15 moves.

2. White and Black

Take 4 black and 4 white checkers (or 4 pennies and 4 other coins) and put them on a table in a row, white, black, and so on. Leave a vacant place at one end which can hold 2 checkers. After 4 moves, all the black checkers should be on one side and the white ones on the other.

A move consists of shifting 2 adjacent checkers, keeping their order, into any vacant space.

3. Complicating the Problem

In the last problem, 8 checkers took 4 moves. Show how 10 checkers take 5 moves, 12 take 6, and 14 take 7.