This is the first of (probably not) many posts where I want to share with all of you (my imaginary website readers) some of my favourite maths puzzles. And I could not start in any other way than by sharing one of my favourites of all time.
I am not aware of the original source of this problem, but it was given to me during some IMO preparation sessions in Barcelona in 2018. It involves the prime numbers and a seemingly complex game, and it struck me for its extraordinarily simple solution.
The number 2 is written on the board. Alice and Bob play a game where they alternatingly increase this number by a quantity between 1 and 1000 (inclusive). The only condition is that the result must be a prime number. The player that cannot complete their turn, loses. Determine who has the winning strategy.