Y-Wing Strategy

This is an excellent candidate eliminator. The name derives from the fact that it looks like an X-Wing - but with three corners, not four. The fourth corner is where the candidate can be removed but it leads us to much more as we'll see in a minute.

Lets look at Figure 1 for the theory.

A, B and C are three different candidate numbers in a rectangular formation. Three of the corners have two candidates AC, AB and BC. The cell marked AB is the key. If the solution to that cell turns out to be A then C will definitely occur in the lower left corner.If AB turns out to be B then C is certain to occur in the top right corner. C is a complementary pair.

So whatever happens, C is certain in one of those two cells marked C. The red C can be 'seen' by both Cs - the cell is a confluence of both BC and AC.
It's impossible for a C to live there and it can be removed.

In Figure 2 I'm demonstrating the sphere of influence two example cells have, marked red and blue. X can 'see' all the red cells, Z can 'see' all the blue ones. In this case there are two cells which overlap and these are 'seen' by both.

If our A, B and C are aligned more closely they can 'see' a great deal more cells than just the corner of the rectangle they make. In Figure 3 BC can see AB because they share the same box. AC can see AB because they share the same row. BC and AC can see all the cells marked with a red C where this Y-Wing can eliminate whatever number C is.

I have found (June 2025) a new 'tough' Sudoku puzzle with a sequence of five Y-Wings to illustrate the full range of this strategy. The first three are pictured here but you can load the puzzle into the solver to see the remaining examples.

The first Y-Wing is a rectangular alignment which is close to the theory diagram. The AB cell in A1 links 7 with the pair on A7 and the 1 in E1. The number common to both the pincer cells is 2 which must go in either A7 or E1 so 2 in E7 can be removed.

The second Y-Wing has four target cells show in pink but three of them are solved cells so of no use. But there is a 7 in C2 that can be eliminated. The 7s in A1 and C5 are linked to A6 by 1 and 2 respectively. One end of the pincer or the other must be 7.

The third step is a similar pincer movement. A6 is connected to A7 by 2 and to B4 by 1. Looking along row B we can remove 7 from B9

So here is a tricky situation. Doesn't seem obvious at first sight which 89 in H6 or H7 could make the Y-WIng. Why did the solver pick H6? Well there is a double and mirrored Y-Wing here. The solver just returned the first. Equally valid is a hinge on J8 and a common candidate 9 allowing 9 to be removed from H6. The result is the same - fixing 8 and 9 on those cells.

Y-Wing Exemplars

These puzzles require the Y-Wing strategy at some point but are otherwise trivial.
All replaced June 2025 except for number 10.
They make good practice puzzles.

• Exemplar 1, x3 (score 80)
• Exemplar 2, x3 (score 103)
• Exemplar 3, x3 (score 104)
• Exemplar 4, x3 (score 112)
• Exemplar 5, x3 (score 112)
• Exemplar 6, x3 (score 117)
• Exemplar 7, x3 (score 123)
• Exemplar 8, x3 (score 125)
• Exemplar 9, x3 (score 130)
• Exemplar 10, x4 (score 146)