MathDB

Two kids

A

and

B

play a game as follows: from a box containing

n

marbles (

n > 1

), they alternately take some marbles for themselves, such that: 1.

A

goes first. 2. The number of marbles taken by

A

in his first turn, denoted by

k

, must be between

1

and

n - 1

, inclusive. 3. The number of marbles taken in a turn by any player must be between

1

and

k

, inclusive. The winner is the one who takes the last marble. Determine all natural numbers

n

for which

A

has a winning strategy

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