MathsJam 2024 - Weekend of November 2nd/3rd
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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.
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