Hearts: Answer to question 19

Q: In yet another game, the scores were in geometric progression. What was the winner's score?

A: 32

The losing score must be a cube or multiple of a cube and be between 100 and 125. The possible combinations are set out below, with the total of the scores and the remainder when that total is divided by 26. Only those combinations with a remainder of 0 represent possible game scores. The last combination is not possible, as the score of 125 means someone had to Shoot the Moon, after which at least three players' scores would be 26 or more.

Ratio    Scores     Total Remainder
2     13 26 52 104    195   13
3/2   32 48 72 108    260    0
3      4 12 36 108    160    4
2     14 28 56 112    210    2
2     15 30 60 120    225   17
5      1  5 25 125    156    0