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Farmer and Wife To Catch Rooster and Hen
Sam Loyd's Puzzle

Here's one of Sam Loyd's puzzles with a little taste of mathematics.

On a New Jersey farm, where some city folks were wont to summer, chicken-chasing became an everyday sport, and there were two pet chickens which could always be found in the garden ready to challenge any one to catch them. It reminded one of a game of tag, and suggested a curious puzzle which I am satisfied will worry some of our experts.

The object is to prove in just how many moves the good farmer and his wife can catch the two chickens.

The field is divided into sixty-four square patches, marked off by the corn hills. Let us suppose that they are playing a game, moving between the corn rows from one square to another, directly up and down or right and left.

Play turn about. First let the man and woman each move one square, then let each of the chickens make a move. The play continues by turns until you find out in how many moves it is possible to drive the chickens into such positions that both of them are cornered and captured. A capture occurs when the farmer or his wife can pounce on a square occupied by a chicken.

The game can be played on any checkerboard by using two checkers of one color to represent the farmer and his wife, and two checkers of another color to represent the hen and rooster.

The applet below simulates the puzzle. To help grasp the essence of the puzzle, the applet gives an option to first try catching one chicken with just one member of the family: the farmer catching the rooster or the wife the hen. While writing the simulation I made an assumption, I believe implicit in Sam Loyd's formulation. Holding on to a live chicken not being a simple matter, a fellow who caught a chicken loses the ability to help out the mate in catching the other bird.

To play, drag a farmer or his wife from one location to another, but only one location left, right, up, or down . When both are present, they both are to be moved before the chickens try to escape their pursuers.

<hr> <h3> This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet. </h3> <hr>

Besides the standard 8×8 board, the applet also allows to play the game on the 7×7 and 6×6 boards.

Solution

References

  1. Mathematical Puzzles of Sam Loyd, Selected and Edited by Martin Gardner, Dover, 1959

Copyright © 1996-2008 Alexander Bogomolny



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