Problem 24 · 2017 Math Kangaroo
Stretch
Logic & Word Problems
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Leonie has hidden a Smiley behind some of the grey boxes. The numbers state how many Smileys there are in the neighbouring boxes. Two boxes are neighbouring if they have one side or one corner in common. How many Smileys has Leonie hidden?
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Answer: B — 5
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Hint 1 of 2
A number in a white box counts the Smileys in its grey neighbour boxes (boxes touching it by a side or a corner).
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Hint 2 of 2
Begin with a number whose grey neighbours are few: it may force every one of them to hold a Smiley.
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Approach: use each clue box to decide which grey boxes hold Smileys
- Each white number tells how many of its touching grey boxes hide a Smiley.
- A clue near an edge has only a few grey neighbours, so a large number there fills them all; a small number elsewhere then forces nearby boxes to stay empty.
- Working clue by clue, every grey box is decided as either holding a Smiley or empty.
- Counting the boxes forced to hold a Smiley gives 5 in total.
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