Some of the problems which come under the heading of “ inferential puzzles ” are useful for illustrating a varied selection of topics in modern mathematics. Consider the following problem.

Tom, Dick and Harry are married to Jane, Mary and Susan, but not necessarily in that order. Each couple has one child; the children's names are Alan, Brenda, and Charlie.

• (i) Mary's child and Harry's child are the two stars of the school football team.

• (ii) Tom's son is not Alan.

• (iii) Dick's wife is not Susan.

• Find who are the parents of each child.

• This problem, unlike some of its type, is easily solved by a straightforward commonsense argument.