Unyielding Totals

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.
Each dotted cage carries a total. The numbers of the cage have this sum and are all different; this prohibition also applies between two cells of the cage that do not share a line, column or block. The few pre-filled figures are part of the problem.

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	2	3	4	5	6	7	8	9
1	9		14				13	22
2	16	18		27		19
3					18			20
4		17							8
5	13		10	18		21
6								19
7	19	19	8		27				156
8					12		11
9		5					2		7

Thick stroke: region. Dotted inside the cells: cage and its total. A tint on a diagonal reminds the diagonal constraint, if it applies.

Exact list of cages (coordinates and totals)

Cage 1: L1C1, L1C2; total 9.
Cage 2: L1C3, L1C4, L1C5, L1C6; total 14.
Cage 3: L1C7, L2C7, L2C8; total 13.
Cage 4: L1C8, L1C9, L2C9, L3C9; total 22.
Cage 5: L2C1, L3C1, L4C1; total 16.
Cage 6: L2C2, L2C3, L3C2, L3C3; total 18.
Cage 7: L2C4, L2C5, L3C4, L4C4; total 27.
Cage 8: L2C6, L3C6, L3C7, L4C6; total 19.
Cage 9: L3C5, L4C5, L5C5; total 18.
Cage 10: L3C8, L4C7, L4C8, L5C8; total 20.
Cage 11: L4C2, L4C3, L5C2; total 17.
Cage 12: L4C9, L5C9; total 8.
Cage 13: L5C1, L6C1, L6C2; total 13.
Cage 14: L5C3, L6C3; total 10.
Cage 15: L5C4, L6C4, L6C5, L6C6; total 18.
Cage 16: L5C6, L5C7, L6C7, L7C7; total 21.
Cage 17: L6C8, L6C9, L7C8, L8C8; total 19.
Cage 18: L7C1, L8C1, L9C1; total 19.
Cage 19: L7C2, L8C2, L8C3, L9C3; total 19.
Cage 20: L7C3, L7C4, L8C4; total 8.
Cage 21: L7C5, L7C6, L8C6, L9C6; total 27.
Cage 22: L7C9, L8C9; total 15.
Cage 23: L8C5, L9C4, L9C5; total 12.
Cage 24: L8C7, L9C7, L9C8; total 11.
Cage 25: L9C2; total 5.
Cage 26: L9C9; total 7.

Why this level?

After unique candidates, single places, bare pairs/triples and interactions between units, the solver still reaches bifurcations. The exhaustive evidence reaches 9 intertwined hypotheses, examines 127 states and closes 63 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 Maybe it's shorter.

Your workspace

Write down your assumptions separately from deductions you have proved.

Notes for SOLO-010

View the solution to SOLO-010 →