by Dave Youngs
This month's Puzzle Corner is a modification of one of the many match stick puzzles that abound in books on recreational mathematics. This particular puzzle comes from the collection of the great British mathematician and puzzlist, H. E. Dudeney ( 1847- 1930). As has been previously noted in this column, there was a tremendous interest in puzzles that could almost be described as puzzle mania around the turn of the last century. This puzzle mania swept Asia, North America, and Europe. Newspapers and magazines carried various mathematical puzzles like the ones that regularly appear in this column in addition to the more traditional crosswords and word jumbles. Since things like radio, television, and video games were pastimes of the future, many people occupied their hands and minds with puzzles like the one presented here.
As with many match stick puzzles, there is a story to go with Penning a Half-Dozen. This story explains that a farmer had a sheep pen made of 13 identical fence pieces which enclosed six sheep pens all of identical shape and size (as pictured on the student page using toothpicks). One night a thief stole one of the fence pieces, leaving the farmer with only 12. How can the farmer rebuild the sheep pens so that there are still six pens of identical shape and size! All of the fence pieces must be used without overlapping or cutting any of them.
This is the challenge with which your students are faced as they solve this problem - to create six equal- sized shapes using 12 toothpicks. Emphasize that they do not need to double up or overlap the toothpicks in any way to correctly solve this. I would encourage you to have your students work on this problem independently so that they can all experience the joy of discovering the solution.
I hope you and your students enjoy this puzzle.