Hearts: Answer to question 3

Q: What is the highest first place score, if no first place ties are allowed?

A: 102

Obviously, if the winner ends up with a score of more than 100, then all players pass 100 only on the last hand (which means that no one Shoots the Moon in that hand). Let's work out some possible scores at the end of the second last hand.

The largest multiple of 26 which is less than 400 is 390.

At the end of the second last hand, this total score of 390 must be shared out between the players so that all have an individual score of less than 100. Even if the others are all 99, one player must have a score of at least 93.

In the last hand, someone gets the Queen of Spades, scoring 13. Even if it is the player on 93 who scores 13, she jumps to 106. The other players have 13 points available between them. The winner (one of those on 99) gets at most 3 of these points if she is to win clearly, meaning her final score is 102. (The other two have a final score of 104.)