Problem
COM-B1-M08-P003 Reach \(21\)
#3
★☆☆☆☆ Level 1 of 5
Players alternately add a number from \(1\) to \(4\) to a total. The initial total is \(0\). Whoever first reaches \(21\) wins. Who wins?
\(21\equiv1\pmod5\).
The first player first adds \(1\). After an opponent move of \(a\), where \(1\le a\le4\), the first player adds \(5-a\). Then after the first player’s moves the totals are \(1,6,11,16,21\). Therefore the first player wins.
Simple model of complement strategy.