Question 153
We say that two permutations $a_{1}, \ldots, a_{4035}$ and $b_{1}, \ldots, b_{4035}$ of the integers $1, \ldots, 4035$ intersect if there exists an integer $k \leqslant 4035$ such that $a_{k}=b_{k}$. We say that a set $E$ of permutations is unavoidable if every permutation of the integers $1, \ldots, 4035$ intersects some permutation belonging to E.
a) Show that there exists an unavoidable set containing 2018 permutations.
b) Does there exist an unavoidable set containing 2017 permutations?
a) Show that there exists an unavoidable set containing 2018 permutations.
b) Does there exist an unavoidable set containing 2017 permutations?