Sly ArcadeSeparate the circle from the sum.
An original lesson from the verified puzzle collection.
The rule
Use ordinary Sudoku units. The digits on a shaft sum to the single circle digit. The circle is not included in that sum.
Read the constraint
For a circle containing 5 with a two-cell shaft, the shaft may contain 1+4 or 2+3 in a legal order. The circle itself is not part of the sum. Start at the circle and follow the arrow tip.
Connect the candidates
A shaft cell may repeat another shaft digit when their ordinary units permit it. Do not import the Killer no-repeat cage rule. The candidates must still fit their own rows, columns and boxes.
Make a justified move
If one shaft cell is 2 and the circle is 7, the other shaft cells together total 5. With an unfilled circle, narrow possible circle values and shaft sums in both directions.
A real puzzle example
Open arrow-sudoku-001, then focus on r1c6. The explanation below is generated from this puzzle’s logical proof, without looking up its answer.
Reveal the explained next step
- The circle equals the sum of the shaft cells. Repeats are allowed when ordinary units permit them.
- The circle equals the sum of the shaft cells. Repeats are allowed when ordinary units permit them.
- The circle equals the sum of the shaft cells. Repeats are allowed when ordinary units permit them.
- The circle equals the sum of the shaft cells. Repeats are allowed when ordinary units permit them.
- Every other digit is excluded by the current units and constraint candidates.
The justified digit is 8.
Practice without a penalty
Use Notes to record options. Undo restores digits and notes together. Hints reveal attention, explanation and conclusion in separate steps. All 200 puzzles are open. A daily selection is a replay from the verified pool, with its own save.
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