Problem 23 · 2017 Math Kangaroo
Stretch
Logic & Word Problems
work-backward
Petra likes even numbers, Ina likes numbers divisible by 3, and Celina likes numbers divisible by 5. A basket holds 8 balls, each marked with a number. Each girl went to the basket alone, in turn, and took every remaining ball that matched her taste. Petra took 32 and 52; Ina took 24, 33 and 45; Celina took 20, 25 and 35. In what order did they go to the basket?
Show answer
Answer: D — Ina, Celina, Petra
Show hints
Hint 1 of 2
Some balls fit two girls' tastes; whoever ended up with such a ball must have visited the basket first.
Still stuck? Show hint 2 →
Hint 2 of 2
Use a shared ball each time to order two girls, then chain the comparisons.
Show solution
Approach: use shared-preference balls to order the visits
- 45 is a multiple of both 3 and 5; Ina took it, so Ina came before Celina.
- 20 is both even and a multiple of 5; Celina took it, so Celina came before Petra.
- Chaining these: Ina, then Celina, then Petra.
- The order is Ina, Celina, Petra (D).
Mark:
· log in to save