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# Math problem

## Using logic to make the sale

An encyclopedia salesman calls at a home. The woman who answers the door says she'll buy something from him if he can give the ages of her three children. The first clue, she says, is that the three ages multiplied together equal 36. He responds that he needs more information, so she says that the three ages add up to the number of the bus that passed by. He thinks for a while and says he needs one more clue. So she says, my youngest child has red hair, and then he is able to answer and make his sale. What are the ages of the three children? (HINT: The salesman needed all three clues to get an answer.)

ANSWER: There are eight combinations of three numbers that multiply together to make 36: 36x1x1, 18x2x1, 3x12x1, 9x4x1, 6x6x1, 2x2x9, 6x2x3, 3x3x4. Since the man needed more information after discovering the ages added up to the bus number, more than one of these combinations must equal the same number (6+6+1=13 and 2+2+9=13). The third clue enabled him to answer because she said she had a youngest child. If the ages were 2, 2, and 9, she'd have youngest children (plural) so it makes sense that the answer is 1, 6, and 6. This problem is from Bill Handley, an Australian who wrote the math-help book "Teach Your Children Tables." He says sixth- or seventh-graders should be able to solve it because the math that's required is basic. Many students and adults find it difficult, he says, but the problem shows how people can be taught to reason and think logically.