Problem 23 · 2018 Math Kangaroo
Stretch
Logic & Word Problems
caseworklogic
Lea should write the numbers 1 to 7 in the fields of the figure, one number per field. Two consecutive numbers may not be in adjacent fields. Two fields are adjacent if they share an edge or a corner. Which numbers can she write in the field with the question mark?
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Answer: E — the numbers 1 or 7
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Hint 1 of 3
Remember that two fields count as touching if they share an edge OR even just a corner, and numbers that come right after each other (like 4 and 5) may not touch.
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Hint 2 of 3
Count how many other fields the question-mark field touches — it touches almost all of them, with only one field not touching it.
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Hint 3 of 3
Think about how many close-by partners each number has: 1 and 7 have just one each, but the numbers in the middle have two.
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Approach: count the neighbours of the marked field and see which numbers have few enough consecutive partners
- The marked field touches 5 of the other 6 fields; only one field does not touch it.
- So a number placed there can have at most one of its consecutive partners (one less and one more) kept away from it.
- A number from 2 to 6 has two partners, but there is only one safe spot for them, so those numbers cannot go there.
- Only 1 (whose only partner is 2) and 7 (whose only partner is 6) work, so the answer is the numbers 1 or 7.
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