MathDB

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:

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B

takes one pebble from each cup and redistributes them as

A

wishes.

\bullet

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.

\bullet

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

Problem Statement