Problem 13 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintmagic-square
The numbers from 1 to 6 are placed in the circles at the intersections of 3 rings. The position of the number 6 is shown. The sum of the numbers on each ring is the same. What number is placed in the circle with the question mark?
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Answer: A — 1
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Hint 1 of 2
Add 1..6 to get 21; each circle lies on two rings, so the three ring-sums add to twice 21.
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Hint 2 of 2
That fixes every ring's sum; use the given 6 to pin down the marked circle.
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Approach: use the common ring sum
- The numbers 1..6 add to 21, and every circle sits on exactly two rings.
- So the three equal ring-sums total 2×21 = 42, making each ring sum to 14.
- Working from the fixed 6 and the requirement that each ring totals 14 forces the marked circle.
- The question-mark circle holds 1, choice (A).
Mark:
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