Cross-sum runs
Combine crossing sum constraints while checking repeats within each run.
Logic & rule checking
- Players
- 1–3 cooperatively
- Time
- 10–20 minutes
- Materials
- Two 2×2 number grids, row/column clues and pencil.
Prepare
Each puzzle is a 2×2 white-cell block. Fill digits 1–9. Each horizontal pair must sum to its row clue and each vertical pair to its column clue. No repeated digit within either pair. The same digit may appear diagonally because diagonal cells are not one run.
Play
Start with puzzle 1 row sums 4,6 and column sums 3,7. Pencil candidate pairs before choosing. Check a candidate against both its crossing clues. You cannot use zero or repeat a digit just because the numerical sum matches. All four filled cells must be checked together.
Worked example
Rows [1,3] and [2,4] solve puzzle 1:4/6 across and 3/7 down. Trying [2,2] for the first row is forbidden by the repeat rule. Puzzle 2 has row sums 7,11 and column sums 5,13; [1,6] and [4,7] is one valid answer.
Finish and check
A completed valid grid wins cooperatively. Puzzle 1 has a unique answer under these rules; puzzle 2 intentionally permits alternatives. Find a second solution to puzzle 2 or explain how your candidate fails a constraint. Finish after both grids are audited.
Adaptation and limits
Use enlarged cells, a partner scribe or a list of pairs summing to each clue. This is a small run-sum introduction, not the publisher’s commercial puzzle or an automatic solver. A host should validate all constraints rather than reject an alternative solely for differing from the sample.
Purpose, observation and provenance
Within this activity: Combine crossing sum constraints while checking repeats within each run.
Ask for a reason for each digit; do not promise every puzzle has one solution.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Nikoli — Kakuro — Run-sum and no-repeat rule background; our two tiny grids are independently constructed.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Cross-sum runs
Puzzle 1 rows 4,6; columns 3,7. Blank 2×2.
Puzzle 2 rows 7,11; columns 5,13. Blank 2×2; seek two answers.
| 3 | 7 | |
|---|---|---|
| 4 | ___ | ___ |
| 6 | ___ | ___ |
| 5 | 13 | |
|---|---|---|
| 7 | ___ | ___ |
| 11 | ___ | ___ |
Player record · keep the host key separate
| Puzzle | Candidate | Clue checked |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Host key · separate from players
P1 [1,3;2,4]. P2 examples [1,6;4,7] and [2,5;3,8].
Run the round
Each puzzle is a 2×2 white-cell block. Fill digits 1–9. Each horizontal pair must sum to its row clue and each vertical pair to its column clue. No repeated digit within either pair. The same digit may appear diagonally because diagonal cells are not one run.
Start with puzzle 1 row sums 4,6 and column sums 3,7. Pencil candidate pairs before choosing. Check a candidate against both its crossing clues. You cannot use zero or repeat a digit just because the numerical sum matches. All four filled cells must be checked together.
Rows [1,3] and [2,4] solve puzzle 1:4/6 across and 3/7 down. Trying [2,2] for the first row is forbidden by the repeat rule. Puzzle 2 has row sums 7,11 and column sums 5,13; [1,6] and [4,7] is one valid answer.
A completed valid grid wins cooperatively. Puzzle 1 has a unique answer under these rules; puzzle 2 intentionally permits alternatives. Find a second solution to puzzle 2 or explain how your candidate fails a constraint. Finish after both grids are audited.
Use enlarged cells, a partner scribe or a list of pairs summing to each clue. This is a small run-sum introduction, not the publisher’s commercial puzzle or an automatic solver. A host should validate all constraints rather than reject an alternative solely for differing from the sample.
Related activities
Activity library · Four-symbol Latin grid: rules and printable materials