Question 49
Clara and Isabelle choose an integer $n \geqslant 1$ and put $n$ candies in a bowl. They alternate turns, Clara first. If the bowl contains $k$ candies, the player chooses an integer $\ell$ coprime to $k$ with $\ell \leqslant k$ and eats $\ell$ candies. The other player then moves. Whoever eats the last candy wins.
For which $n$ does Clara have a winning strategy?
For which $n$ does Clara have a winning strategy?