by Dave Youngs
This month’s Puzzle Corner activity is patterned after the classic match-stick puzzles which are an important part of the field of recreational mathematics. These puzzles come out of a rich historical tradition that dates back to the nineteenth century when matches were first manufactured. Invented in 1827 by the British chemist, John Walker, matches soon replaced the tinder boxes that people had formerly used to light fires. As matches became ubiquitous later in the century, they spawned a new form of entertainment—match-stick puzzles—which became quite popular when several match companies printed these puzzles on their boxes. Capitalizing on this interest, publishers began to print books of match-stick puzzles. By the early twentieth century, many people had developed a personal repertoire of these puzzles which they used to challenge friends and acquaintances.
In match-stick puzzles, the challenge is to move and/or remove a certain number of matches to create a new shape or arrangement. Doing this is easier for students who have well-developed spatialrelationship skills. Often, these students are not the top students in other areas, and their ability to solve these puzzles faster than their peers is a great esteem builder. Conversely, this type of puzzle often frustrates those students who usually do well at traditional school tasks, and provides them with a real challenge. This role reversal is often beneficial for both sets of students.
For safety’s sake, the puzzle presented here uses paper clips instead of matches. Each student will need nine small paper clips and copies of the two activity sheets. The challenge in Penning Ponies is to move only two of the interior pen sections (paper clips) so that the four original pens become three pens holding various combinations of ponies. For each of the combinations listed, there is at least one way to do this without any paper clips sticking out into the middle of a pen. When students get a solution, they should make a record of it on the sheet provided.
Penning Ponies (436k pdf file)
I hope that you and your students enjoy this challenge.