Problem 24 · 2015 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintcasework
Riki wants to write one number in each of the seven sections of the diagram pictured. Two zones are adjacent if they share a part of their outline. The number in each zone should be the sum of all numbers of its adjacent zones. Riki has already placed numbers in two zones. Which number does she need to write in the zone marked “?”?
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Answer: C — 6
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Hint 1 of 2
Each zone equals the sum of its neighbours; write that relation for every zone.
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Hint 2 of 2
Use the two given numbers and the diagram's adjacencies to solve for the zone marked with a question mark.
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Approach: solve the adjacency-sum equations
- Label the seven zones; each value equals the sum of the values in the zones touching it.
- Using the placed numbers and the adjacency relations from the figure gives a small system of equations.
- Solving it forces the '?' zone to equal 6.
- So Riki writes 6 (C) in the marked zone.
Mark:
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