Solving arrows
The circle equals the sum of the arrow. So the smallest the arrow can add up to is the smallest the circle can be, and a small circle keeps every arrow digit small.
Why it works
On the board above:
The arrow runs from the circle in r5c5 through r5c6, r5c7 and r5c8. The circle equals their sum.
The three arrow cells share row 5, so they must be different digits.
The smallest three different digits are 1, 2 and 3, which add up to 6.
So r5c5 can only be 6, 7, 8 or 9.
More moves
Repeats lower the floor
Arrow cells that don’t share a row, column or box can hold the same digit. Then the smallest sum is lower.
r6c2 and r7c3 are in different rows, columns and boxes, so both can be 1.
That makes the smallest sum 2, not 3.
So r5c1 can be anything from 2 to 9.
A small circle caps the arrow
Once you know the circle, the arrow has to add up to it. A small total leaves very few digits.
The circle r8c1 is 4. Two different digits that make 4 are 1 and 3.
Column 2 already has a 3, in r2c2, so r8c2 can’t be 3.
So r8c2 is 1 and r8c3 is 3.
How to use it
Find the smallest sum
Fill the arrow with the lowest digits it allows. Cells that share a row, column or box must be different.
That is the circle’s floor
The circle can’t be less than that sum.
Work back from the circle
The circle is at most 9. Take away the smallest the other arrow cells can be, and that caps each cell.
Use the givens
A known circle or arrow digit turns the sum into a small puzzle with few answers.
Practice
8 boards. Each has one right answer, checked by our solver.
Loading the boards…
Try it in a real puzzle
Each of these starts with arrow sums.
Tips
Three cells in a line
Three arrow cells that see each other add up to at least 6, so the circle is 6 to 9.
Repeats are allowed
Arrow digits can repeat when the cells don’t share a row, column or box. That lowers the floor.
A small circle is a gift
A circle of 3 on a two-cell arrow means the arrow is 1 and 2.
Look for long arrows
A long arrow with a single-digit circle has very few ways to add up.