The 45 rule
1 + 2 + … + 9 = 45. Every complete row, column and box therefore totals 45. If whole cages cover all but one cell, subtract their sums from 45 to find the missing digit. If they cover the entire region plus an extra cell, subtract 45 from the cage sums to find that extra digit.
Worked example
Whole cages cover eight cells in a row and their totals add up to 41. The row totals 45, so its ninth cell is 45 − 41 = 4. In this example the cages must not extend outside the row.