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Here are some puzzles ... don't expect them all to have clear answers, or even to be well-defined! * Show that the sum (yes, the sum) of two consecutive odd primes always has at least three (not necessarily distinct) prime factors. * What proportion of numbers don't have the digit 9? * If a bacterium divides in two with probability /p/ and dies the rest of the time, starting with one bacterium, what is the probability that the population dies out entirely? * In how many ways can you dissect a square into congruent pieces that all touch the centre point? * Can you dissect a square into congruent pieces such that: ** The centre of the square is in the interior of one of the pieces; ** The pieces don't have all straight sides. * Can you solve the previous puzzle with a triangle instead of a square? * Find all configurations of four points in the plane that between them define exactly two distances. * Find three integers in arithmetic progression whose product is a prime. Do you have a favourite puzzle? Contact us and maybe we can include it here.