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Tue, 17 Sep 2019

What techniques are there for solving mosaic puzzles?

The more you solve mosaic puzzles, the more interesting solving methods you find.

There are two key methods however for solving mosaic puzzles.

The first is the most obvious and intuitive - if there is only one possible way that the cells can be coloured to meet the given value of a cell then those cells can be marked in straight away.

Thus a nine in a cell can always be filled in immediately - colour the cell and its eight touching neighbours, as there is only one way to fill in 9 of 9 cells!

Also do the opposite with 0's : either put a dot or a small 'x' in each of the nine cells around the 0 so you know that none of those are filled.

With many puzzles you will need to do some simple cross-referencing to whittle down the options that are possible for two givens that influence each other.

As a common example, imagine you have this arrangement:

xxx
x63
xxx

here the 'x' simply represents an empty cell rather than one you know not to contain a value. Now we can see that the '3' and the '6' have six common cells between them. This means we know a maximum of three of these can be filled. This means all three cells in the left hand column must be filled in order to meet the requirement that six cells around the given 6 must be filled in.


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