There are 10 cups, each having 10 pebbles in them. Two players A and B play a game, repeating the following in order each move:∙ B takes one pebble from each cup and redistributes them as A wishes. ∙ After B distributes the pebbles, he tells how many pebbles are in each cup to A. Then B destroys all the cups having no pebbles.∙ B switches the places of two cups without telling A.After finitely many moves, A can guarantee that n cups are destroyed. Find the maximum possible value of n.
(Note that A doesn't see the cups while playing.)Proposed by Emre Osman combinatoricsGame Theorycombinatorial game theoryolympic revenge