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by Dave Youngs.
The Puzzle Corner activity this month is an adaptation of a classical
matchstick puzzle from recreational mathematics. As has been noted before in
this column, these puzzles date back to the nineteenth century when matches
were first manufactured and began to proliferate. Most matchstick puzzles can
be broken into two general categories: those that are geometric in nature, and
those that aren't. The original version of The Goalpost Puzzle fits in
the latter category and is one of the harder non-geometric puzzles. Persistence
and an ability to "think outside of the box" are usually required to solve it.
If your students are veteran puzzlesolvers, you might want to challenge them
with the original puzzle which is described below.
To do the classic version of this puzzle you need four toothpicks and a small
object like a penny. Place the penny on a flat surface and arrange the toothpicks
around it to form a goalpost. Without touching the penny, you must re-form the
goalpost in another positionÑso that the penny is no longer between the uprightsÑby
moving only two toothpicks.
The Goalpost Puzzle presented here differs from the classical matchstick
brainteaser in two ways. First, flat toothpicks are used instead of matchsticks
for safety reasons. Second, an attempt has been made to make the puzzle a little
bit easier so that it isn't too frustrating for students. To do this, students
are presented with two challenges instead of the original puzzle's one. The
first challenge is to reorient the goalpost by moving three toothpicks. This
is easy to do and gets them used to the mechanics of the puzzle. After this
initial success, they are better pre pared for the second (original) challengeÑreorienting
the goalposts by moving only two toothpicks.
To do The Goalpost Puzzle, each student will need four toothpicks and
a copy of the student sheet. Students then follow the written instructions and
begin working on the puzzle. They should be able to quickly solve the first
challenge, which has a number of different solutions. The second challenge,
how ever, will probably take some time (and perseverance) for most students.
Encourage students who solve this second challenge not to share the solution
with others. If they show others the solution, it will rob those who have not
discovered the solution of the satisfaction of solving the puzzle for themselves.
Worksheet As always, the answer to this puzzle will appear next month. This is done intentionally
so that you don't accidentally see the solution before trying the puzzle yourself.
This is especially important with this puzzle since once someone sees how it
is done, it seems so simple that he or she is surprised it is considered difficult.
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