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A-Point-ing Pennies

A-Point-ing Pennies

This week’s Puzzle Corner activity is a one-person game with a fascinating history that goes back thousands of years and spans three continents. Dominic Olivastro, in the book Ancient Puzzles, notes that archeologists found three curious etchings on the roof slabs of the ancient Egyptian temple at Kurna which date back to around 1400 BCE. Olivastro conjectures that these etchings, which are very different from the heiroglyphics and symbols in the rest of the temple, were carved by ancient stonemasons as a form of entertainment. One of these etchings, a five point star, represented a board for a common game of the day. While the masons carved no instructions for playing the game, Olivastro points out that this game has survived and is still played in Greece today, and that it is highly likely that this game is one of many that the ancient Greeks “borrowed” from Egypt. Olivastro also points out that the Spanish, who probably learned the game from the Greeks, took it with them to Mexico during the colonial period. In time, this game spread to Native Americans throughout North America. It is fascinating to realize that as you and your students work on this game, you will be trying to solve a puzzle that has been around for about 3400 years.

PenniesEach student will need nine pennies and a copy of the student sheet for this puzzle. If you do not have enough pennies for the whole class, beans, buttons, or other small objects will also work. The challenge in this puzzle is to get as many pennies on the star as possible. A penny can be placed on the star by beginning on an empty point (as identified by a number) and moving two spaces along a straight line to another empty point. Pennies may jump over other pennies if necessary, as long as they begin and end on an empty point.

While it is fairly easy to get six pennies on the star, seven is a bit harder, eight is difficult, and nine is the ultimate challenge. Students should be encouraged to find and record as many solutions as they can which get at least seven pennies on the star. You may want to have extra copies of the solutions sheet for those students who discover more than six solutions.

The ultimate challenge of nine pennies on the star may prove to be a difficult task for some of your students. This particular puzzle, however, has the advantage of being a good model for alternative methods of solution. If students are repeatedly unsuccessful at getting nine pennies on the star and are growing frustrated, you may want to suggest that they attempt a method other than trial and error, such as working backwards. Hopefully some students will think of this method on their own and discover its usefulness as a problem-solving technique.

Begin by placing a penny at any of the numbered points on the star. Move that penny two points along a straight line to another empty point. For example, you could begin by placing a penny at 9 and moving it to either 7 or 3. Repeat this process until you can’t get any more pennies on the star. Pennies may jump over the other pennies, if necessary, as long as they begin and end on an empty point. The ultimate challenge is to get nine pennies on the star, but if you can get seven or eight, you’ve done pretty well. Try to get as many different solutions as possible. Record each solution that gets at least seven pennies on the star.

Star

Solution

Click the arrow below to view the solution.

Below are two possible solutions to the “A-Point-ing Pennies” puzzle.

Move
Point to Point
 
Move
Point to Point
1
5
3
1
7
1
2
8
5
2
10
6
3
2
8
3
9
7
4
4
2
4
4
10
5
10
4
5
3
9
6
6
10
6
2
4
7
1
6
7
5
3
8
7
1
8
8
5
9
9
7
9
8
2

 

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