Up to Something

• Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.

• Dynamic Fog: The grid is covered in fog. Correctly placing a digit will clear any fog in its own cell, and potentially clear fog in other cells too. No guessing is required.

• Up to Given-sums: Each row, column, and 3x3 region contains exactly one given digit whose exact location is to be deduced. No two givens are identical digits, i.e. each of the digits 1 to 9 is given exactly once.

A clue outside a row or column indicates the sum of all digits up to the given digit. (The given digit itself is not included in the sum.)

• Arrows: Digits on an arrow sum to the digit in the circle from which the arrow emerges.

• Kropki: Digits joined by a black dot have a 1:2 ratio. Digits joined by a white dot are consecutive. (Not all dots are given.)