THE SHIFT
Beginners see a Kakuro run summing to 17 across two cells and start adding pairs in their head: 8+9, 9+8. That works but it's slow.
Experienced solvers see "17 in 2 cells" and just know the only pair is {8, 9}. They've internalised the combinations. That's the shift.
THE MAGIC SUMS
Some clue + run-length combinations have only one possible digit set. Memorise these and a third of every Kakuro puzzle solves itself.
2 cells:
3 → {1, 2}
4 → {1, 3}
16 → {7, 9}
17 → {8, 9}
3 cells:
6 → {1, 2, 3}
7 → {1, 2, 4}
23 → {6, 8, 9}
24 → {7, 8, 9}
4 cells:
10 → {1, 2, 3, 4}
30 → {6, 7, 8, 9}
The pattern: extreme low or extreme high clues lock the digit set. Mid-range clues have multiple options, so save those for after you've used the magic sums to anchor the grid.
CROSS-REFERENCE
Every cell sits in two runs — one horizontal, one vertical. The cell's digit has to be in both runs' possible sets. The intersection is usually one or two digits.
A 17-in-2 horizontal run shares {8, 9}. The vertical run it crosses might allow {1, 2, 3, 5, 6, 8}. The only overlap is 8 — that cell is 8.
This is where Kakuro actually gets solved. Magic sums set up the candidates; cross-referencing eliminates them down to a single digit.
NO REPEATS, USE THE NO-REPEATS
A digit can't appear twice in a run. If a 4-cell run sums to 10 and you've placed a 2 in one cell, the remaining 3 cells sum to 8 with no 2 — so {1, 3, 4} or {1, 4, 3} (same set, different order).
The no-repeats rule is what makes Kakuro deducible. Without it, sums would be ambiguous. With it, every constraint cuts the candidate space hard.
WHEN YOU'RE STUCK
Two checks before reaching for a guess:
- Did you write out the possible digit sets for every run? Most stuck-feelings come from solving in your head when the candidate space is too big.
- Did you cross-reference every filled cell against every crossing run? A single placed digit usually eliminates options three or four cells away.
If both checks come back clean and you're still stuck, you've almost certainly miscalculated a sum. Audit every placed cell against its two run totals.