How Shared finish works

Shared finish settles a tile by finding the animal common to every valid completion of its line. It follows from both of Pawmoku's rules. In the first 45 library puzzles it decides 3 tiles, in 3 of the boards. Its earliest use there is step 15 of 8x8 puzzle 16.

Why it works

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

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

An eight-tile line needs four of each animal and no three in a row. Exactly three finishes fit this example: DCCDDCDC, DCDCDCDC and DCDCDDCC, where C means cat and D means dog. All three start with a dog.

When to look for it

Look at a line where pairs, gaps and counting have not settled the next tile. Keep only finishes that follow both rules and every animal already placed.

Three line examples

Example 1

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

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

Example 2

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

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

Example 3

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

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

Find it in practice

8x8 Puzzle 4: Shared finish first decides a tile at step 23.
8x8 Puzzle 10: Shared finish first decides a tile at step 30.
8x8 Puzzle 16: Shared finish first decides a tile at step 15.