# How to finish off a sudoku with lots of options?

The Sudoku below has difficulty approx 4/10, so it's supposed to be quite simple.

However, I'm stumped.

Can someone give me some tips here? I'm not looking for the solution, only strategies for how I can solve this as easily as possible.

I can of course do a manual brute force by hand, but I'm hoping there are more elegant ways to go about it.

That difficulty rating of 4/10 should be much higher!

The only way forward from here (verified online) is

Using an XY-Wing - an advanced sudoku technique which definitely shouldn't be appearing at 4/10 difficulty!

Filling in all candidates to make things easier to see, there is still no clear way forward.

But using an XY-Wing, we see the following:

Consider the cell in orange. If it is a 4, the 2 blue cells must be a 1 and a 2 respectfully. But then in that case, the green cell cannot be 1 or 2 - which is a contradiction, so the orange cell cannot be a 4.

This allows you to place a number and it should be back to normal sudoku difficulty from there.

According to multiple online checkers that I've cross-checked with, this is the only possible way forward - so very tricky!

• Personally, I consider it poor design to ramp up the difficulty at the very end of a sudoku. Skilled solvers will find the start of the puzzle boring and beginner solvers will feel frustrated that they got stuck on an "easy" sudoku. It makes for a very unsatisfying experience. Commented Aug 5 at 15:15
• I think I prefer if you start your reasoning with the green cell. If that's a 1, then the top blue has to be a 4. If the green cell is a 2, then the right blue cell has to be a 4. In both cases, there cannot be a 4 in the orange cell. I prefer (and think it's easier) if we avoid contradictions. Commented Aug 5 at 17:53
• @Lezzup up to solver preference I reckon - I personally prefer looking for things that aren't possible, but totally get the reverse and looking for things that have to be instead! Commented Aug 5 at 19:08
• @Brian nowadays many sudoku are low-effort in terms that they are simply computer generated. I think it's quite possible for a sudoku to be publish online without being checked or solved by hand. As such a sudoku is likely to have no designer at all. Ratings are also given by a program. Commented Aug 6 at 10:45
• "This is the only possible way forward" isn't perfectly accurate. You can also make the deduction: "If r7c9 were a 4, then r5c9 is a 2, so r2c9 is a 1, so r3c8 is a 4, so now r5c8 has zero options. Therefore r7c9 is a 1." This is a bilocation link on 5 cells that one may or may not consider simpler than the mentioned XY-wing. Commented Aug 7 at 1:24