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Kakuro for Beginners: Sums Without Repetition
Kakuro is the number-lover’s crossword: every horizontal and vertical run must add to its clue, using digits 1–9, never repeating a digit inside one run.
1. The one non-negotiable rule
A run may not repeat a digit. That single rule is what makes totals like 4 in two cells instantly equal 1+3 or 3+1 — never 2+2. Everything else in Kakuro follows from it.
2. Learn a few fixed sets
Memorise the totals that have exactly one combination. In two cells: 3 (1+2), 4 (1+3), 16 (7+9), 17 (8+9). In three cells: 6 (1+2+3), 7 (1+2+4), 23 (6+8+9), 24 (7+8+9). When you see these clues you already know the digits, and the crossing run tells you which order they go in.
3. Start small, not big
Clues of 3, 4, 6, 7, 16, 17, 23 and 24 narrow to a single set. Fill those first. Large mid-range clues like 11 or 12 have many combinations and should wait until crossings eliminate most of them.
4. Respect the crossing
Every cell belongs to two runs at once. When you pencil candidates into a cell, the digit must satisfy both the horizontal sum and the vertical sum. This double constraint is where solutions fall out: a cell that only fits one digit in each direction settles itself.
5. Keep tidy notes
Write small candidate digits in each cell and cross them off as runs fill. A run of length three with clue 8 can be 1+2+5, 1+3+4 or 2+… — the crossing clue is what prunes the list.
6. Use the errors to teach
The game flags a run that has overshot its clue or repeated a digit immediately. Treat those highlights as free information: a run over its total means one of the digits you pencilled is wrong, so revisit the crossing cells rather than guessing a replacement.