Problem
COM-B1-M08-P016 Reach \(100\)
#16
★★★☆☆ Level 3 of 5
Players alternately add a number from \(1\) to \(9\) to a total. The initial total is \(0\). Whoever first obtains \(100\) wins. Who wins?
\(100\) is divisible by \(10\), so the control totals belong to the second player.
After each first-player move of \(a\), the second player adds \(10-a\). Then after the second player’s moves the totals are \(10,20,30,\ldots,100\). Therefore the second player reaches \(100\) and wins.
Same complement strategy, but the second player wins.