Square coins?

Discrete Mathematics Level pending

A pile of coins is on the table.

Two players alternate picking \(n\) coins from the table, where \(n\) must be a square number. For example, if there are 10 coins on the table, you could take 1, 4 or 9 coins.

The player to take the last coin (or a group containing the last coin) wins!

Martha realizes that if it's her turn, and there are 22 coins in the pile, she can't guarantee a win.

What is the next number greater than 22 for which if it is your turn you will lose assuming both players play optimally?

If you think there are no such numbers, i.e. every number greater than 22 will guarantee you a win, then please provide 0 as the answer.


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