## Monday, March 28, 2016

### Solution to Spring 2016 POTW #2 (Weird? You Bet!)

See here for the original post of the puzzle.

Trial and error may work here, but I don't recommend it. Instead:

• Suppose Adam starts with \$A and Brendan with \$B
• Adam loses first game, pays out to double Brendan's money.
• New results: Adam has \$(A-B)\$ and Brendan has \$(2B).
• Brendan loses second game, pays out to double Adam's money.
• New results: Adam has \$(2(A-B))=\$(2A-2B) and Brendan has \$(2B-(A-B)) = \$(3B-A).
• By assumption: 120 = 2A-2B = 3B-A.
• Solve this system of equations to get A=150 and B=90.
Playing it out, just to check:
• Start: Adam has \$150, Brendan has \$90.
• Adam loses. New results: Adam has \$60, Brendan has \$180.
• Brendan loses. New results: Adam has \$120, Brendan has \$120.
(Here's a bonus challenge for you readers: Is there anything special about \$120? Could this puzzle be solved for any ending amount? And what if there were 3 players and each one lost a round? Try to generalize!)