Tapa: clue fit and clue pairs
List every way a clue’s runs can sit around it. Whatever all of them agree on is certain. When one clue isn’t enough, check it against a neighbor.
How it works
A tapa clue lists the runs of shaded cells among the 8 cells around it. A 3 is one run of three. 1 3 is a run of one and a run of three, with white cells between them.
To use a clue, picture every way its runs could sit around it, given what is already marked. If every way shades a cell, it is shaded. If none does, it is white. That is clue fit.
Some clues are free. A 0 makes all eight cells around it white. An 8 shades all of them. Clues on the edge or beside other clues have fewer cells, so they fit fewer ways.
When a clue still has several fits, compare it with a clue that shares some of its cells. Fits that leave the neighbor no way to work are ruled out.
Counting fits
Go around the ring in order and slide the runs along it. A single run of k fits in up to 8 places in the middle of the grid. Several runs fit fewer ways, because each needs a white gap after it.
Cells off the edge and clue cells are white, so they break the ring and cut the count down fast. That is why edge and corner clues are good places to start.
Worth memorizing
A 0 makes its ring white, an 8 makes it wall.
Every fit agrees on a cell: that cell is settled.
This is clue fit.
Two clues sharing cells must agree.
A fit that leaves its neighbor no way is out.
Practice
0 of 4 rightWhat is the ringed cell?
On an empty board, how many ways can the ringed clue fit around its cell?
Using clue fit on one clue at a time, what is the ringed cell?
Now compare the 2 with the 1 1. What is the ringed cell?