The Missing Ballot

Very Hard — logic-grid deduction puzzle

The signed ballot for the finals' most valuable player went missing, and only the clerk's notes were left to show who got which votes.

The night the finals ended, the arena counted the votes for the finals' most valuable player. Four names were left on the ballot: Maximiliano, Percival, Rolando and Jermaine. Each of them got a different number of first-place votes (18, 23, 25 or 36, from fewest to most), and each had scored a different number of points in the deciding game. The clerk lined the four names up by first-place votes and wrote a side tally next to each one. A side tally was the deciding-game points of the player just above him in that line and the player just below him, added together. The players at the top and the bottom of the line had only one neighbour, so their side tally was just that one neighbour's points. Then the signed ballot went missing, and the clerk's notes were all that was left.

Clues

1. The guard's side tally came to 56.
2. In the line-up by first-place votes, the player who scored 35 stood between the one who scored 30 and the one who scored 22.
3. Either the wing got 36 first-place votes, or the forward scored 26 in the deciding game. Only one of these was true.
4. On first-place votes, the wing had one of the top two counts: 25 or 36.
5. In the deciding game, the wing scored one of the two lowest totals, 22 or 26.
6. Maximiliano outscored both Percival and Rolando in the deciding game.
7. Jermaine had one of the two middle vote counts, 23 or 25 first-place votes.
8. Only one of these was true: Maximiliano was the guard, or Percival got 18 first-place votes.

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