Notes in the Heat

Hard — logic-grid deduction puzzle

Steam in the tunnel smudged the referee's notebook, and only his margin notes can still sort out the cards shown to Casimir, Dagoberto, Eamon and Lysander.

The knockout was played on a scorching day, and by full time the steam in the tunnel had made the ink in the referee's notebook run. Casimir, Dagoberto, Eamon and Lysander were each shown one card, each at a different minute and for a different offence. Each had also run a different distance by the time his card came out. The referee kept two extra notes in the margin. The first was a heat-load for each booking, which grew as the afternoon got hotter: 1 at minute 19, 2 at minute 44, 3 at minute 67, and a full 5 at minute 83. The second was a neighbour tally. He lined up the four distances from shortest to longest, 9.5, 10.4, 11.2 and 12.1 km. For each player, he added up the heat-loads of the players whose distances sat just before and just after his in that line. The shortest and the longest runner had only one neighbour each, so their tally was that one neighbour's heat-load. Only the margin can still be read: use it to put all four back together.

Clues

1. Casimir's heat-load added to Lysander's, less Dagoberto's, came to zero.
2. Casimir's card came between Lysander's card and Eamon's card.
3. Eamon's neighbour tally came to 8.
4. The neighbour tally beside Dagoberto's line read 1.
5. Either Lysander had run 11.2 km by the time he was booked, or he had run 9.5 km.
6. Only one of these was true: Eamon was booked for handball, or Casimir was booked for time wasting.
7. Either Lysander or Dagoberto was the player shown the card for late tackle.
8. The card for time wasting came out later than the card for late tackle.

Play this puzzle

Read the clues, rule out what cannot be, and prove what must be. Every GRIDIGMA puzzle is verified by a solver that shows the reasoning behind each step, so a solution is never a guess.

All GRIDIGMA puzzles

Logic grid puzzles: how to solve them, with a worked example