\section*{Exercise 1 - 101011}

Two students \(A\) and \(B\) play the following game.

From a pile of exactly 150 matches, both must alternately take matches, and each must take at least 1 match but no more than 10 matches, with \(A\) starting. The winner is the one who can take the last match.

Determine which of the two can force a win, and explain how they can achieve it with certainty!
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For a simple illustration, consider the reverse problem, where one starts with 0 matches and adds them.

If \(A\) sets out 139 matches, \(B\) must play, and \(A\) then has a number from 140 to 149 in front of him, from which he can win. How can \(A\) safely set out 139?

By setting out 128 beforehand; working backwards, thus \(117, 106, 95, 84, 73, 62, 51, 40, 29, 18, 7\), i.e., \(A\) plays 7 in the first move, in the second he adds enough to make it 18, etc.