None of these puzzles is easy. If you solve all them then you are probably a genius. Some have been the subjects of papers and recent debates in philosophical journals. These puzzles are more than just amusing ways to challenge the gray matter. They show us how easily our thinking goes wrong, in particular, how often we make unwarranted assumptions. They give us useful warnings and sharpen our mental skills. A deceptively simple problem, such as the two envelope paradox, shows how easily we can reach a wrong conclusion. This and other paradoxes suggest that there may be many times when we think things through, apparently with sufficient care, but arrive at the wrong conclusion.

The solutions illustrate some important principles of logical reasoning.

How do you tell that you have blue eyes?

The Travellers' Dilemma: a decision paradox that still puzzles game theorists.

Why does the moon appear larger when near the horizon? This illusion still baffles the boffins. Written and posted in November 2013.

Why does the number 1 occur as the first digit 6.5 times more often than 9 in data as varied as electricity bills, lengths of rivers, and rotation rates of pulsars? Benford's Law.

How to cross the bay without sexual pecadillos puzzle.

The deceptive prize swap paradox.

The formidable and famous Two Envelope Paradox is a simple but very challenging conundrum, one that the philosophers are still arguing about.

An elementary but tricky three card puzzle

The disappearing 13th man visual puzzle

Lateral thinking: a medley of short puzzles.

Bertrand's Paradox in simple probability.

Newcomb's Paradox: the philosophers are still arguing about this one.

The Monty Hall Puzzle: a difficult puzzle on probability.

The Liar's Paradox: a classical Greek paradox that tormented and inspired Bertrand Russell.

Birds of diverse feathers: a difficult multiple-choice test devised by Tad Boniecki.

A ternary duel: whom would you shoot first?

Proof that 2 = 1 and other mathematical foolishness.

U2 in a hurry: can you maximise their bridge crossing capability?

The Prisoners' Dilemma: a famous decision paradox.

The St Petersburg Puzzle: an infinitely expensive gamble.

The Sleeping Beauty Problem is a difficult but elementary problem in probability.

If all the above were too easy then have a go at the Millenium Problems.