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The Goalpost Puzzle

The Goalpost Puzzle

The Puzzle Corner activity this week 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 position so that the penny is no longer between the uprights by 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) challenge reorienting 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.

Place four toothpicks on the outline of the goalpost below. Note that in this position
the football is in the middle of the upright arms.

Challenge 1: Move three toothpicks and reorient the goalpost so that the football is no longer in the middle of the goalpost’s arms.

Challenge 2: Replace the toothpicks in their original positions. Now, try to do the same thing by moving only two toothpicks.




Click the arrow below to view the solution.

In The Goal Post Puzzle, students were challenged to move exactly two toothpicks in a goalpost arrangement and re-orient the goalpost so that the picture of the football was no longer in the middle of the goalpost’s arms. One solution appears below.

Goalpost Solution

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