Problem 19 · 2020 Math Kangaroo
Hard
Algebra & Patterns
sum-constraintsubstitution
Beatriz has five sisters whose ages are 2, 3, 5, 8, 10 and 17. Beatriz writes these ages in the circles of the diagram so that the sum of the ages in the four corners of the square equals the sum of the ages in the four circles in the horizontal row. What is this sum?
Show answer
Answer: D — 32
Show hints
Hint 1 of 2
The left and right circles belong to both groups, so when you set the two sums equal those two ages cancel out.
Still stuck? Show hint 2 →
Hint 2 of 2
That leaves top + bottom = centre + far-right; find the split of the six ages that makes this work, then add up the four corners.
Show solution
Approach: cancel the two shared circles, then place the rest
- The corners (top, left, right, bottom) and the horizontal row (left, centre, right, far-right) share the left and right circles, so equal sums mean the unshared pairs match: top + bottom = centre + far-right.
- Among 2, 3, 5, 8, 10, 17 the pairs 3 + 10 and 5 + 8 both make 13, so put 3 and 10 at top and bottom, and 5 and 8 at centre and far-right.
- That leaves 2 and 17 for the shared left and right circles. Each sum is then (left + right) + (the matching 13) = (2 + 17) + 13 = 32.
Mark:
· log in to save