Page 56: Figure It Out
Q1. Can the children rearrange themselves so that the children standing at the ends say ‘2’? Answer: No. Reasoning: A child says ‘2’ only if both neighbors are taller. Children at the ends of the line only have one neighbor. Therefore, they can say ‘0’ (if taller than neighbor) or ‘1’ (if shorter), but never ‘2’.
Q2. Can we arrange the children in a line so that all would say only 0s? Answer: Yes. Reasoning: If all children are of the exact same height, then no neighbor is taller. The definition of ‘0’ is “neither neighbor is taller”.
Q4. There are 5 children of different heights. Can they stand such that four say ‘1’ and the last says ‘0’? Answer: Yes. Arrangement: Ascending order (Shortest to Tallest).
- Child 1 (Shortest): Neighbor is taller. Says 1.
- Child 2: Left is shorter, Right is taller. 1 neighbor taller. Says 1.
- Child 3: Left is shorter, Right is taller. 1 neighbor taller. Says 1.
- Child 4: Left is shorter, Right is taller. 1 neighbor taller. Says 1.
- Child 5 (Tallest): Left is shorter. No right neighbor. 0 neighbors taller. Says 0.
Q7. How would you rearrange five children so maximum number say ‘2’? Answer: We want as many “valleys” (short children between tall ones) as possible. Arrangement: Tall - Short - Tall - Short - Tall
- Ends (Tall): Say 0.
- Inner Shorts: Both neighbors are Tall. They say 2.
- Inner Tall (Middle): Both neighbors are Short. Says 0. Max number of ‘2’s is 2.