Problem
COM-B1-M12-P015 Set 4. Total \(50\)
#15
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Players alternately add a number from \(1\) to \(6\) to a total. The initial total is \(0\). Whoever first obtains \(50\) wins. Who wins?
\(50\equiv1\pmod7\).
The first player adds \(1\). Then after an opponent move \(a\), the first adds \(7-a\). After the first player’s moves the totals are \(1,8,15,\ldots,50\), so the first wins.
Complement strategy.