The Stubborn Mirror

Complete the grid completely. Only one solution respects all constraints.

Materials: Pencil and gum; no commercial material.

Rules you need

Fill in the 81 boxes with numbers from 1 to 9. Each row and column contains each of the nine digits exactly once.
The coordinates L1C1 to L9C9 are read from the top left corner. No calculation is made on the coordinates numbers.
Each of the nine blocks of 3 × 3 also contains numbers 1 to 9 without repetition.
The two large diagonals each contain numbers 1 to 9 without repetition. This constraint adds to the blocks.

The puzzle

The empty boxes are to be completed. The given numbers are fixed. The answer and proof are on another page.

Coordinates: lines from top to bottom, columns from left to right.
L / C	1	3	4	5	6	7	8	9
1					2		1	3
2	4		6			8		9
3				4
4
5					6
6	7	1	4
7	5			6	9	7
8
9			1	2	5

Why this level?

After single candidates, single places, bare pairs/triples and interactions between units, the solver still reaches bifurcations. The exhaustive evidence reaches 9 intertwined hypotheses, examines 37 states and closes 18 branches by contradiction. The Extreme level combines eliminations of candidates and deep branched analysis; this is not a ranking based on the number of empty boxes. Editorial evaluation according to the protocol of the collection, without calibration on a panel of players; another logical path can be made to the extent that it is possible to be shorter.

Your workspace

Write down your assumptions separately from deductions you have proved.

Notes for SOLO-006

View the solution to SOLO-006 →