Thinking Skills
Owen, Paz and Quinn each have 22 beads. They take turns: even means give that many to each of the other two; …
Question 1 · Multiple choice
Question
Owen, Paz and Quinn each have 22 beads. They take turns: even means give that many to each of the other two; odd means receive that many from each. Owen spins 4. Paz spins 1. If they end with 15, 30 and 21, what did Quinn spin?
Options
- A. 1
- B. 2
- C. 3
- D. 4
Correct answer
B. 2
Explanation
Everyone starts with 22 beads. Owen spins 4. Since 4 is even, Owen gives 4 beads to Paz and 4 beads to Quinn. So Owen loses 8 altogether. New totals: Owen 14, Paz 26, Quinn 26 Paz spins 1. Since 1 is odd, Paz receives 1 bead from Owen and 1 from Quinn. So Paz gains 2 altogether. New totals: Owen 13, Paz 28, Quinn 25 Now test Quinn's possible spin. To finish on 15, 30 and 21, Quinn must lose 4 altogether, while Owen and Paz each gain 2. That happens when Quinn spins 2, because 2 is even and he gives 2 to each of the other two. Check: Owen 13 + 2 = 15 Paz 28 + 2 = 30 Quinn 25 - 4 = 21 So Quinn spun 2.