Last cell in a cage
When every cell of a cage but one is filled, the missing digit is simply the sum minus what is already there.
What it is
This is the most direct move in Killer Sudoku. A cage of three cells summing to 15 with 4 and 9 already placed leaves 15 − 13 = 2. No candidate analysis is needed; the arithmetic decides.
How to spot it
After every digit you place, glance at its cage. If only one empty cell remains, subtract the placed digits from the cage sum and write the result.
Worked example
Step through the example. First the position, then the cage the argument rests on, then the candidates, and finally what follows from it.
Step 1 of 4: The starting position
- Pattern cells
- 8/6, 9/6
- Digits
- 2
- Follows from it
- 9/6
Press a marked square to point it out on the board above.
Why it matters
A cage's digits add to a fixed total. If all but one are known, the remaining value is determined by subtraction. The only check needed is that the result is between 1 and 9 and does not repeat a digit already in the cage — and if the puzzle is valid, it will be.
Practise now
The practice puzzle is picked so that this technique is what gets the solve moving again.
Frequently asked questions
Is this really a technique?
It is the one you will use most. Every digit you place potentially completes a cage, and each completed cage hands you another digit for free.
What if the subtraction gives a digit already in the cage?
Then one of the placed digits is wrong. In a correct grid this cannot happen, so it works as a useful self-check.
What if the result is above 9 or below 1?
Same thing: an earlier entry must be wrong. It is a good moment to undo and re-check the cage.
Put it to use
Where you will meet it
Medium grids are where this move starts to matter: the obvious cells run out and the pattern takes over.
Play MediumStuck on a grid of your own?
Type the position into the solver and it walks the whole solution, naming the technique behind every step — including this one.
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