Problem 22 · 2024 Math Kangaroo
Stretch
Logic & Word Problems
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The picture on the right shows a honeycomb with 9 cells. Some cells contain honey. The number written in a cell tells how many of its neighbouring cells contain honey. How many cells are filled with honey?
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Answer: C — 6
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Hint 1 of 3
Each written number counts how many of that cell's touching neighbours hold honey — like a honey version of Minesweeper.
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Hint 2 of 3
Start at a cell with few neighbours: if a clue equals its number of neighbours, every one of them must be honey.
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Hint 3 of 3
Use each filled-in clue to force its neighbours, one cell at a time, until the whole comb is settled.
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Approach: use each clue to decide its neighbours, starting where a clue forces everything
- Begin at an edge cell whose clue equals its number of touching neighbours — then all of those neighbours must hold honey.
- Once those are fixed, neighbouring clues tell you which of their remaining cells are honey and which are empty.
- Keep applying the clues, cell by cell, so that every number ends up matching the honey around it.
- When the whole comb is consistent, six of the cells contain honey: 6 (C).
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