Arrow Sudoku: How to Solve Sums Along a Path
An Arrow Sudoku has circles with lines leaving them. The digit in a circle is the sum of the digits on its arrow. The circle is not part of that sum.
That last sentence is the one worth keeping in view. If a circle holds 7 and its arrow passes through three cells, those three cells add to 7. They do not add to 14, and the circle does not use up one of the cells on the path.
The rules that do not change
Every row, column, and 3×3 box still contains 1 to 9 once each. Start with ordinary Sudoku when those rules are new, then return to the arrows once a candidate list is familiar.
Start from the smallest possible total
An arrow is a sum, but it is also a bound. A two-cell arrow can be as small as 3: 1 + 2. A three-cell arrow can be as small as 6: 1 + 2 + 3. Repeated digits would already fail a row, column, or box whenever the arrow cells share one, but the arithmetic alone is enough to rule out many circle values.
Here the circle is 5. One body cell already holds 3, so the other has to be 2. The circle itself is not included: 3 + 2 makes 5.
This is the useful way to read an arrow early: do not wait for every arrow cell to be solved. Ask what combinations could possibly make the total.
A known arrow cell changes the whole path
The next board has a 6 in its circle and a known 4 on its path. The other body cell has to be 2. The row, column, and box rules decide whether that 2 has anywhere left to go.
The row, column, and box rules decide whether those small digits have anywhere left to go. That is why Arrow Sudoku feels more connected than a single-cell clue. A placement on one end of a path can change the candidates several cells away.
Do not treat a path as an ordered calculation
The line tells you which cells belong to the sum. It does not say that their digits rise or fall as the line travels across the grid. That is a Thermometer rule, not an Arrow rule. A 1, 4, 2 path and a 2, 4, 1 path make the same total.
Keep the two jobs separate: arrows provide an exact total, while normal Sudoku decides which position can take each digit.
Try it
Use the short-arrow puzzle below without the answers. The two circles each name the total of the cells on their path.
Where to go next
Renban also marks a line of cells, but asks for a consecutive set rather than an exact sum. Thermometer uses a path in the other direction: its digits must rise from bulb to tip.
If you want the version where most of the grid is hidden while you solve, fog of war Sudoku is that. Everything published so far is on the Learn index.
Sudoku Fog is on Android — What Sudoku Fog is, Get it on Google Play.