Thinking Skills
Liam, Macy and Niamh each have 20 coins. They take turns: even means give that many to each of the other two;…
Question 1 · Multiple choice
Question
Liam, Macy and Niamh each have 20 coins. They take turns: even means give that many to each of the other two; odd means receive that many from each. Liam spins 2. Macy spins 3. If they end with 12, 27 and 21, what did Niamh spin?
Options
- A. 1
- B. 2
- C. 3
- D. 4
Correct answer
A. 1
Explanation
Everyone starts with 20 coins. Liam spins 2. Since 2 is even, Liam gives 2 coins to Macy and 2 coins to Niamh. So Liam loses 4 altogether. New totals: Liam 16, Macy 22, Niamh 22 Macy spins 3. Since 3 is odd, Macy receives 3 coins from Liam and 3 from Niamh. So Macy gains 6 altogether. New totals: Liam 13, Macy 28, Niamh 19 Now test Niamh's possible spin. To finish on 12, 27 and 21, Niamh must gain 2 coins, while Liam and Macy each lose 1. That happens when Niamh spins 1, because 1 is odd and she receives 1 from each of the other two. Check: Liam 13 - 1 = 12 Macy 28 - 1 = 27 Niamh 19 + 2 = 21 So Niamh spun 1.