Hitori Solving Techniques

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Must Circle (Dynamic)

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This technique can be very hard to spot, and is similar to the 'Cannot Circle' technique as we are testing for what would happen should we circle each occurrence of a set of the same number in a row or column.

Firstly, look for more than one occurrence of a number in a row or column. Ask yourself what would be the outcome of the next two moves following circling of each occurrence. The key here is to find other cells on the board which would need to be circled, regardless of which of the occurrences you are investigating would be circled.



In the first example, you can see that if the first cell containing the number 5 was circled, the second cell containing the number 5 would need to be painted (set). The 3 in the cell above would need to be circled to prevent a 'corner close'. If however the second cell containing the 5 were circled, the first number 5 would need to be painted (set), and hence as the number 3 in the cell above is adjacent to a painted cell, it would again need to be circled. So from this we deduce that even though we don't know yet which of the 5's will be circled or painted, the number 3 in the cell above will always be circled. This allows us to progress the game.

Here are some more examples: