Unique Rectangle Type 4

Walkthrough

Example 01 — One number is locked to a box

The rectangle numbers are 3 and 4. The two exceptional corners r8c6 and r9c6 share column 6, number 4 appears nowhere else in column 6. Therefore 4 must occupy one of those two corners.

If cell r8c6 were number 3, then number 4 would be pushed into cell r9c6, in turn, cell r8c1 would be 4, and cell r9c1 would be 3, now it would end up with a deadly pattern of four corners' values liking this:

you could swap left and right cornor pairs, or above and below cornor pairs, while the rest of the soduku grid would still be perfeectly valid.

Similarly, if cell r9c6 were number 3, it would end up with the same deadly pattern. Therefore, both cells r8c6 and r9c6 cannot be number 3.

What to notice: The house restriction proves one rectangle number must be present; uniqueness then eliminates the other number.

Walkthrough

Example 02 — Check all shared houses

Similarly, in this example number 3 is forced in column 8 (or box 3), so number 2 can be eliminated from two rectangle cornor cells in column 8.

What to notice: Two exceptional corners can share more than one house, such as a row and a box or a column and a box. You only need one of those houses to contain the required strong placement condition.

If a rectangle number has no other possible location in that house, it must occupy one of the two exceptional cells. That is enough to trigger the uniqueness elimination.

You are not looking for a new candidate pattern; you are proving that one of the existing rectangle numbers is forced into the pair.