Often problems are posed in such a way that making lists of possible solution candidates is an effective strategy. Further information lets you eliminate some of the candidates.

Use this method to solve the following problem.

• I am a two-digit number. (Clue 1)
• The sum of my digits is 11. (Clue 2)
• I am two more than a square number. (Clue 3)
• My tens digit is greater than my ones digit. (Clue 4)
• What number am I?

Here is one way to solve this problem: From Clue 1, we know that the number is one of the 90 numbers 10, 11, . . . , 98, 99. Clue 2 narrows the list to 92, 29, 83, 38, 74, 47, 65, and 56. Clue 3 eliminates all of these numbers except 83 and 38, and only 83 fits Clue 4.

This process, listing all possibilities and eliminating the ones that do not work, more or less "walks" the solver through the solution process. The ability to ask yourself questions and then answer them is a valuable problem-solving skill. When students work in groups, they can question one another. Individual problem solvers must learn to talk to themselves.

This problem is a good example of a problem that is easily adaptable to a variety of concepts and a variety of levels. After experiencing several problems of this type, students often enjoy writing similar problems for their classmates to solve.

  A list of other problem-solving strategies to keep in mind