Problem
COM-B1-M08-P008 Reach \(50\)
#8
★★☆☆☆ Level 2 of 5
Players add a number from \(1\) to \(6\) to a total. The initial total is \(0\). Whoever first obtains \(50\) wins. Who wins?
After the winner’s moves the totals should be \(1,8,15,\ldots\).
Since \(50\equiv1\pmod7\), the first player starts with \(1\). If the second adds \(a\), the first adds \(7-a\). Then after the first player’s moves the total increases by \(7\): \(1,8,15,22,29,36,43,50\). The first player wins.
It is useful to state the full chain of target totals.