Arrow Sudoku Help

Arrow is a variant of Sudoku which adds arrows to the grid. Arrow consists of Sum cell marked with circle and Arrow line cells which have to sum to value in the circle cell. Values on the arrow line can repeat as long as that does not break any other rule.

Arrow Sudoku Solving Strategies

In the image above we can see:

• Green cell must be 5, because arrows with single cell arrow have same sum cell and arrow cell
• Yellow cell must be at least 6 because all 3 cells on the arrow line are in same house (box), which means they cannot repeat. Minimal value for three cells is 1+2+3 which is 6.
• Blue cell must be 9 because we have two cells in box 1 with minimal value of 3 and three cells in box 2 with minimal value of 6. Sum must be at least 9 and it cannot be greater than 9.

Sum cell can have multiple lines, in other words we can have overlapping arrows.

On the image above sum must be at least 5 because we need two ways to make the sum, and there is no more than one way to create 4.

On the image below if we put 1 and restrict it from the arrows, sum must be at least 7, because it is the first digit that can we can create from two sets of digits without using 1 (2+5 and 3+4).

Same logic cannot be applied when arrows are not in same house (row, column or box).

Arrow sum can never contain 1 except in case when arrow line is one cell long and it's not in the same house as the sum cell. Single cell arrow is more or less replacement for short Palindromes.

In come cases we have short arrows which appear unrelated and both can have small sums, but that's not actually the case. On image below we can see one arrow that appears to be able to be 6 and another that appears it can be 3. In this case since all arrow digits are on the same line, minimal sum of the two arrows if 5 unique digits, which is 15 (1+2+3+4+5), which means sum cells must also sum to at least 15. In this case sum cells can be 6,9 or 7,8, or 8,9.

If sum cells don't see each other they can also have 8 and 8.

Below is another example where arrows share a box instead of a row, same logic can be applied to columns, diagonals and windoku windows.