Mathematical Brain Teasers and Logic Puzzles

A few theories on why puzzles are created; Professor Rosenhouse notes that mathematicians love puzzles; warming up with six brain-teasers involving hourglasses, a restaurant order, a biased coin and the numbers on a clock face.

Tackling the puzzle that likely inspires the famous expression "thinking outside the box"; applying this strategy to a variety of brain-teasers; pondering the physics exam question of how one can find the height of a building by using a barometer.

Finding a shortcut solution to a classic word problem in algebra; using cleverness to solve problems without x's and y's; the consequences of having too much information; why transcontinental flights take longer in one direction than the other.

Turning to logic puzzles by trying to distinguish between knights and knaves; starting with simple cases; "if-then" statements; what if the knight or knave is insane; adding a third category of normal people who are sometimes truthful, sometimes not.

Author Lewis Carroll writes a book of logic puzzles for children; taking a crack at some of these exercises; what one can conclude from such categorical statements as "all wasps are unfriendly, and all puppies are friendly"; Carroll's syllogisms.

Puzzles where asking the right questions is the point of the problem; the "heaven or hell" puzzle; closing with an exercise in coercive logic by puzzle master Raymond Smullyan; easy riches hinge on a simple bargain that sounds too good to be true.