Problem 23 · 2023 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintwork-backward
A teacher wants to write the numbers from 1 to 7 into the circles, exactly one number in each circle. When he adds up the two numbers of circles that are next to each other, he gets the number written between those two circles. Which number does he write in the circle with the question mark?
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Answer: D — 4
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Hint 1 of 2
The number sitting between two circles is just those two circles added together.
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Hint 2 of 2
Start with a gap whose two circles you can guess, then fill the circles one at a time like a chain.
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Approach: treat each in-between number as the sum of its two circles and fill the chain step by step
- Each number written between two circles is the sum of the two circles next to it, and the seven circles use 1 through 7 once each.
- Begin at a gap where only one pair of circle numbers can add up to it, write those in, then move along filling each next circle so its new gap matches.
- When the chain is complete, the circle with the question mark holds 4.
Mark:
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