# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Lying Brain Teasers: Politicians, Liars and Mathematical Puzzles," by John Allen Paulos. abcnews.com, 7 December 2003.

Prompted by a series of recent bestselling politically partisan books, Paulos presents three tricky puzzles having to do with lies and lying---which relate to ideas in logic, probability, and number theory. The first puzzle, made popular by logician Raymond Smullyan, is adapted to a scenario in which each politician either always tells the truth or always lies; the second puzzle concerns politicians each of whom tells the truth 1/4 of the time, lying at random 3/4 of the time; and the third puzzle involves a politician who lies at times "but then becomes conscience-stricken and makes it a point never to tell two lies in succession." Paulos then presents the three solutions. He provides hints, using logic, probability and number theory---not full explanations---to keep the reader thinking.

*--- Annette Emerson*