In Coin-cerned about Change there are three film canisters labeled 10 cents, 15 cents, and 20 cents. Each of the canisters contains two coins. Once has two dimes, one two nickels, and one a nickel and a dime. Each canister is mislabeled. The challenge in this puzzle is to determine exactly what coins are in each of the mislabeled canisters by looking in only one. After students have discovered a way to do this, they communicate how they solved the problem.
This month's Puzzle Corner activity is a logic problem. Even though logic is an important topic in mathematics, these types of problems are often avoided by elementary teachers and textbooks alike. I have found that elementary students can succeed at logic activities and that many even enjoy them. Coin-cerned about Change should be easy enough for most elementary students to solve if they are given appropriate encouragement and time.
Logic puzzles like this one are normally presented at the abstract level as thought problems. While this is all right for adults and those students who are good at abstract thinking, I have found that most elementary students need concrete aids. For this problem, I make up several sets of film canisters for groups of students to use when working on a solution. This seems to help and many of my fourth, fifth and sixth grade students have been able to solve this problem, and its extension, using the canisters. I suggest that you make at least one set of canisters, or other similar canisters, when doing this problem with your students.
This puzzle has an interesting extension that makes it a bit more challenging. The extension asks if you can find a way to correctly determine the contents of the canisters by seeing only one coin from one canister. While the logic involved in solving the extension is a bit more difficult than the logic needed to solve the original problem, I have found that older students can do the extension after they have thought through the original puzzle.
We hope that you enjoy this puzzle.
Good luck and have fun!