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Daily calcudoku

Wednesday, 16 September 2026 · 6×6 Medium

The puzzle

The 6×6 grid for 16 September 2026, unsolved 6+ 1− 3− 15× 8× 9+ 18× 100× 120× 60× 12× 6+ 2 3 6

Fill every row and every column with the digits 1 to 6, each exactly once, so that the digits in every outlined cage combine to its target with its operation. This one has 3 addition cages, 2 subtraction cages and 7 multiplication cages.

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Where to start

3 cells are printed for you: a 2 at row 3, column 6; a 3 at row 4, column 2; and a 6 at row 6, column 1. Fill those in first, then let each one rule its digit out of its row and column.

The first moves a careful solver finds:

  1. Work the 100× cage: with what the board already holds, only 5 can sit in row 3, column 3 and still hit the target.
  2. Work the 100× cage: with what the board already holds, only 4 can sit in row 4, column 3 and still hit the target.
  3. Work the 100× cage: with what the board already holds, only 5 can sit in row 4, column 4 and still hit the target.

How this grid gives way

Of the 33 cells left to fill after the 3 printed ones, 18 by a cage’s arithmetic leaving only one value that fits; 14 by crossing off what a cell’s row and column already hold until one digit was left; and 1 by finding the one place left in a line where a digit could still go. No step needs a guess: every Cages daily is checked to have exactly one solution, reachable by reasoning alone.

The full solution

Show all 33 steps
  1. Work the 100× cage: with what the board already holds, only 5 can sit in row 3, column 3 and still hit the target.
  2. Work the 100× cage: with what the board already holds, only 4 can sit in row 4, column 3 and still hit the target.
  3. Work the 100× cage: with what the board already holds, only 5 can sit in row 4, column 4 and still hit the target.
  4. Cross off what the row and column already rule out, and row 4, column 1 has exactly one candidate left: 1.
  5. Cross off what the row and column already rule out, and row 3, column 1 has exactly one candidate left: 3.
  6. Work the 18× cage: with what the board already holds, only 6 can sit in row 3, column 2 and still hit the target.
  7. Cross off what the row and column already rule out, and row 4, column 5 has exactly one candidate left: 2.
  8. Cross off what the row and column already rule out, and row 4, column 6 has exactly one candidate left: 6.
  9. Somewhere in this line the 6 must go — and row 1, column 4 is the only cell that can still take it.
  10. Work the 3− cage: with what the board already holds, only 3 can sit in row 1, column 3 and still hit the target.
  11. Work the 15× cage: with what the board already holds, only 3 can sit in row 2, column 6 and still hit the target.
  12. Work the 9+ cage: with what the board already holds, only 6 can sit in row 2, column 5 and still hit the target.
  13. Work the 9+ cage: with what the board already holds, only 1 can sit in row 3, column 5 and still hit the target.
  14. Cross off what the row and column already rule out, and row 1, column 5 has exactly one candidate left: 5.
  15. Work the 15× cage: with what the board already holds, only 1 can sit in row 1, column 6 and still hit the target.
  16. Cross off what the row and column already rule out, and row 3, column 4 has exactly one candidate left: 4.
  17. Work the 60× cage: with what the board already holds, only 6 can sit in row 5, column 3 and still hit the target.
  18. Work the 12× cage: with what the board already holds, only 1 can sit in row 5, column 4 and still hit the target.
  19. Cross off what the row and column already rule out, and row 2, column 4 has exactly one candidate left: 2.
  20. Work the 8× cage: with what the board already holds, only 1 can sit in row 2, column 3 and still hit the target.
  21. Cross off what the row and column already rule out, and row 5, column 5 has exactly one candidate left: 3.
  22. Work the 12× cage: with what the board already holds, only 4 can sit in row 6, column 5 and still hit the target.
  23. Cross off what the row and column already rule out, and row 5, column 6 has exactly one candidate left: 4.
  24. Work the 120× cage: with what the board already holds, only 5 can sit in row 6, column 6 and still hit the target.
  25. Cross off what the row and column already rule out, and row 6, column 2 has exactly one candidate left: 1.
  26. Cross off what the row and column already rule out, and row 6, column 3 has exactly one candidate left: 2.
  27. Work the 6+ cage: with what the board already holds, only 3 can sit in row 6, column 4 and still hit the target.
  28. Work the 6+ cage: with what the board already holds, only 2 can sit in row 1, column 1 and still hit the target.
  29. Work the 6+ cage: with what the board already holds, only 4 can sit in row 2, column 1 and still hit the target.
  30. Cross off what the row and column already rule out, and row 1, column 2 has exactly one candidate left: 4.
  31. Cross off what the row and column already rule out, and row 2, column 2 has exactly one candidate left: 5.
  32. Cross off what the row and column already rule out, and row 5, column 1 has exactly one candidate left: 5.
  33. Work the 60× cage: with what the board already holds, only 2 can sit in row 5, column 2 and still hit the target.
Show the finished grid
The solved grid for 16 September 2026 6+ 1− 3− 15× 8× 9+ 18× 100× 120× 60× 12× 6+ 2 4 3 6 5 1 4 5 1 2 6 3 3 6 5 4 1 2 1 3 4 5 2 6 5 2 6 1 3 4 6 1 2 3 4 5