Problem 12 · 2024 Math Kangaroo
Hard
Logic & Word Problems
careful-countingcasework
Anna, Bella, Che and Dimitry each have three shapes. Each child shares exactly one of their shapes with one other child. Anna has a triangle, a circle and a square; Bella has a heart, a square and a star; Che has a star, a triangle and a diamond. Which three shapes does Dimitry have?
Show answer
Answer: E
Show hints
Hint 1 of 3
Write out the shapes the other three children have and see which ones already come in matching pairs.
Still stuck? Show hint 2 →
Hint 2 of 3
Some shapes already appear for two children (a pair), but a few shapes appear for only one child so far.
Still stuck? Show hint 3 →
Hint 3 of 3
Dimitry must hold exactly the shapes that still need a partner, so that every shape ends up shared by two children.
Show solution
Approach: give Dimitry the shapes that still need a matching partner
- Among Anna, Bella and Che, the square (Anna & Bella), the star (Bella & Che) and the triangle (Anna & Che) already come in pairs.
- That leaves the circle (only Anna), the heart (only Bella) and the diamond (only Che) without a partner.
- So Dimitry must have the circle, the heart and the diamond — this pairs every shape with exactly one other child, which is option E.
Mark:
· log in to save