# MathsJam 2023 - Weekend of November 11th/12th

### If you need a residential ticket, email us for the waiting list.

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.