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by Michelle Youngs
The Puzzle Corner activity this month comes from the great puzzlist
Martin Gardner. In his book Perplexing Puzzles and Tantalizing Teasers,
this game appears with the title The Dime-and-Nickel Switcheroo. Six
squares are shown forming a two by three rectangle. In every square but one
a coin is to be placedÑthree pennies, one dime, and one nickel. The object of
the puzzle is to switch the dime and the nickel using the fewest possible moves.
A coin can only move by sliding into an adjacent empty spot to the right, left,
up, or down (no diagonals).
As Gardner notes, this puzzle is easy to do if you slide the coins for long
enough; the challenge is to solve the puzzle in the fewest possible moves. This
kind of puzzle is ideal for the elementary classroom and beginning puzzle solvers
because it allows for success at every level. If a student can improve upon
his or her original solution, success has been achieved (assuming it wasn't
solved in the fewest number of moves on the first try).
Gardner gives some broad guidelines concerning the best possible solution saying,
"It can be done in fewer than 20 moves, but it takes more than 12." I would
encourage you not to give your students this information until they have already
discovered at least one solution and improved upon it. That way their sense
of achievement will not be diminished if their original solution did not come
close to the best solution.
I would also encourage you to try this problem yourself before giving it to your
students. See how long it takes you to discover the best possible solution. It is
always good to be able to empathize with students as they go through the
problem-solving experience. Not only will you appreciate their task much more,
you will be better able to guide their discovery without giving away the answer.
Although this puzzle calls for coins, other small objects can be substituted
as long as there are three distinct types. Colored tiles, beans, buttons, or
other small manipulatives will all work equally well. Each student should have
a set of manipulatives to use while working on the puzzleÑyou can even have
the necessary coins brought from home the day before so that the puzzle can
be taken home and shared with families when students are finished with it.
Worksheet We hope that you and your students enjoy this classic puzzle! |
