Locked Squares in Logic Grid Puzzles
Going further, part 4 of 5 of How to Solve Logic Grid Puzzles.
Sometimes you can't tell which of two items goes in a square, but you can tell that one of them must. That is enough to cross the square out for everything else. Puzzle Baron calls this a staggered pseudo-true pair.
The example is Holiday Trips, another puzzle from the app. It has five friends, five activities, and the years 2001 to 2005. Here it is part-way through.
Two friends and the year between them
Clue 5. The trip with Lillie was 1 year after the holiday with Samuel.
Look at what is left for these two friends in the top-left grid.
- Samuel: 2003, 2004 and 2005 are crossed out, so his trip was in 2001 or 2002.
- Lillie: 2001, 2004 and 2005 are crossed out, so her trip was in 2002 or 2003.
Lillie's trip was exactly 1 year after Samuel's, and that leaves only two ways for it to work:
- Samuel in 2001 and Lillie in 2002
- Samuel in 2002 and Lillie in 2003
In both, one of the two friends took the 2002 trip. So 2002 is locked: it belongs to Samuel or Lillie, and nobody else can have it.
What it leads to
Gladys's column now has four X's, so her trip was in 2003. That leaves only 2002 for Lillie, and then only 2001 for Samuel, exactly one year apart as clue 5 requires.
How to spot it
Find a greater-than clue with an exact gap whose two items each have two or three squares left. List the ways the clue can still work. If the same square is used in every one of them, cross it out for all the other items in that row.
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