Problem
COM-B1-M11-P015 Reach \(64\)
#15
★★★☆☆ Level 3 of 5
Players alternately add a number from \(1\) to \(7\) to a total. The initial total is \(0\). Whoever first obtains \(64\) wins. Who wins?
\(64\) is divisible by \(8\).
After the first player adds \(a\), the second adds \(8-a\). Then after the second player’s moves the totals are \(8,16,24,\ldots,64\). Therefore the second player wins.
The control totals belong to the second player.