This month’s puzzle is designed to foster math-ematical thinking as students apply problem-solving skills. In this activity, students are presented with the following paradoxical scenario: Two students each pick four whole numbers less than 10 and multiply them to �nd the product. Although the chosen numbers are not all identical, the products are the same. The challenge in this Puzzle Corner activity is to �nd out how this is possible and to come up with several sets of numbers that work.
This activity is written using precise mathematical vocabulary. Students need to know that whole numbers are the natural numbers (1, 2, 3, 4, …) with the addition of zero (0, 1, 2, 3, …). They also need to know that a product is the answer obtained when multiplying.
In addition to thinking mathematically and knowing the correct vocabulary, students will need to employ some problem-solving strategies in order to solve this paradox. One of the most-used strategies is guess and check, and this is an appropriate one to start with. Some students may get lucky and accidentally �nd a solution, but others will have to employ some other strategies in order to be successful. A few of the strategies that can be used are organizing the data, logical thinking, and using mathematical reasoning. Each of these strategies can help students �nd a solution to this paradox.
As with all Puzzle Corner activities, you should try come up with your own solution(s) before assigning it to your students. This will give you an idea of what students will be facing when tackling this problem. In addition, be sure to remind students to work on this problem independently and tell those who �nd solutions to keep these solutions to themselves until the sharing session later in the week. This way they won’t spoil the joy of discovery for their classmates.