Problem 13 · 2024 Math Kangaroo
Medium
Logic & Word Problems
sum-constraintwork-backward
The 7 cards numbered 1 to 7 are placed in these four overlapping rings. In every ring the numbers on the cards add up to 10. What number is on the card with the question mark?
Show answer
Answer: A — 1
Show hints
Hint 1 of 3
The two end rings hold only two cards each, so start there: each of those pairs must add to 10.
Still stuck? Show hint 2 →
Hint 2 of 3
Once the 6 and the 3 give away their ring-partners, only three cards are left for the three middle spots.
Still stuck? Show hint 3 →
Hint 3 of 3
Use a middle ring (three cards adding to 10) to pin down the question mark.
Show solution
Approach: fill the two-card end rings first, then a three-card middle ring
- The left ring has just 6 and its neighbour, and must total 10, so that neighbour is 4; the right ring has 3 and its neighbour, so that one is 7.
- The cards 6, 4, 7, 3 are now placed, leaving 1, 2 and 5 for the three middle spots.
- A middle ring holds 4, then a card, then the question mark, and must total 10, so (card) + (?) = 6; the other middle ring holds the question mark, a card, and 7, so (?) + (card) = 3.
- Only ? = 1 makes both work (with 5 and 2 in the other spots), so the question-mark card is 1 (A).
Mark:
· log in to save