A hard question on queues for P4–P5, with a step-by-step solution, diagrams and the answer. Queue questions are already in the Hua Xia Cup's P1 and P2 first rounds, and the P4 papers add square formations.
The question
At sports day the pupils form a solid square: as many rows as children in each row, with no gaps.
The outer two layers hold 56 children in all.
How many children are in the square?
Show the hints (3)
💡Hint 1: If each side of the outer layer had 10 children, how many would the outer layer hold? Watch the corners.
💡Hint 2: One layer in, each side has 2 fewer. How many fewer in that layer?
💡Hint 3: The outer layer holds 32. How many on each of its sides?
Worked solution
Have a go first, then read the solution step by step.
1.A layer with m on a side holds 4 × (m − 1) (don't count corners twice). One layer in has 2 fewer a side, so 8 fewer children.
2.Outer + (outer − 8) = 56, so the outer layer = (56 + 8) ÷ 2 = 32.
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