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What technique am I missing here? I have try all the usual naked pairs etc.


You can apply a technique called Simple Colouring. I have underlined some of the candidate ones with either red or blue. The idea is that, supposing the red ones are correct, the blue ones must be false.

If the red one in the top-center box is correct, the blue one in the top-right box must be false, which puts a definite red one into the lower-right box, and thus a blue one into the lower-center cell of the lower-left box.

Similarly, our assumption of the red one in the top-center box denies any other ones in that box (in this case, the blue one in the top-center cell). This results in a red one directly below it in the bottom-center cell, and a blue one in the center-top cell of the lower-left box.

But wait a minute! All candidates for the one in the lower-left cell have been declared blue (impossible), which is contradictory. As such, the locations of the red ones cannot be correct. This means that the lower-left cell of the center-top box must be a six, along with the lower-left cell of the lower-right box.

From there, I believe the rest of this sudoku should be smooth sailing.

simple colouring

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