Combining Two Greater-Than Clues

Going further, part 2 of 5 of How to Solve Logic Grid Puzzles.

When two greater-than clues mention the same item, compare the clues with each other. Together they can tell you something that neither says alone. Puzzle Baron calls these comparative relationships.

The example is All-Star Hockey, another puzzle from the app. It has five players, five teams, and goal totals from 6 to 10. Here it is part-way through.

The same distance from the same item

Clue 4. The person from the Monsters scored 3 goals less than Yang.

Clue 5. The person from the Monsters scored 3 goals less than the player from the Bears.

Both clues measure from the Monsters player. Yang scored exactly 3 more than him, and so did the Bears player. Each goal total belongs to one player only, so two different players can't both be 3 above the same score. Yang and the Bears player are the same person.

Neither clue mentions Yang and the Bears together, which is why this is easy to miss. It helps to scan the greater-than clues for any item that appears in two of them.

Other ways two clues combine

Two greater-than clues can also give you an X. Call the item that both clues mention the shared item.

• Opposite sides. One clue puts A below the shared item and the other puts B above it. Then A and B are different.
• Different distances. A is 3 above the shared item and B is 2 above it. Then A and B are different.

There is one more case, where the clues share no item at all.

• The same gap from two items in one category. A is 2 above C, and B is 2 above D, where A and B are in the same category. A and B are different, so C and D must be different as well.

In each case, put an X where the two items meet, provided they are in different categories.

Next: No options in common
Previous: A second look at either/or and pair clues
All parts of the guide