How Last spare works

Last spare keeps a line's last needed animal of one kind out of any tile where it would force three of the other kind together. It follows from both of Pawmoku's rules. In the first 45 library puzzles it decides 102 tiles, in 32 of the boards. Its earliest use there is step 4 of 6x6 puzzle 15.

Why it works

Before: cat, empty, empty, empty, cat, empty.

After: cat, empty, empty, empty, cat, dog.

This line needs one more cat. A cat in the last tile would use up that last spare cat and force the three middle empty tiles to be dogs. That would make three dogs in a row, so the last tile is a dog.

When to look for it

Look when a line has just one cat or one dog left to place. Check what each candidate would force into the remaining empty tiles.

Three line examples

Example 1

Before: cat, empty, empty, empty, empty, cat.

After: cat, dog, empty, empty, dog, cat.

Example 2

Before: dog, dog, cat, empty, empty, empty.

After: dog, dog, cat, empty, empty, cat.

Example 3

Before: cat, empty, empty, cat, empty, empty, empty, cat.

After: cat, dog, dog, cat, empty, empty, empty, cat.

Find it in practice

6x6 Puzzle 1: Last spare first decides a tile at step 13.
6x6 Puzzle 3: Last spare first decides a tile at step 5.
8x8 Puzzle 1: Last spare first decides a tile at step 30.