Problem 28 · 2025 Math Kangaroo
Stretch
Spatial & Visual Reasoning
caseworkgrid
Martin wants to fill the cells in the diagram so that each cell contains either a cross or a circle, with no row, column or diagonal containing four consecutive identical symbols. What will the grey column contain in the completed diagram?
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Answer: B — 2 circles and 4 crosses
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Hint 1 of 2
No row, column or diagonal may hold four of the same symbol in a row — that rule forces almost every empty cell once you start from the ones already filled.
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Hint 2 of 2
Work cell by cell from the given symbols; whenever three matching symbols line up, the fourth must be the opposite one.
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Approach: propagate the no-four-in-a-row constraint
- Start from the already-filled cells and apply the rule: whenever a line would otherwise get four equal symbols in a row, the next cell is forced to be the other symbol.
- Chasing these forced choices through the grid fills the grey column uniquely.
- The grey column ends up with 2 circles and 4 crosses, which is (B).
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