A hard question on most and least for P4–P5, with a step-by-step solution, diagrams and the answer. Finding the most and the least appears in the Hua Xia Cup from the P1 and P2 first rounds to the P6 papers.
The question
A café cook fries French toast in one pan.
The pan holds at most 2 slices at a time.
Each slice must be fried on both sides, 6 minutes a side (flipping, putting in and taking out take no time).
What is the fewest minutes needed to fry 6 slices?
Show the hints (3)
💡Hint 1: How many sides need frying in all? How many can one round (6 minutes) fry at most?
💡Hint 2: First find the fewest rounds possible. Then think: how can you arrange it so nearly every round is full?
💡Hint 3: List every slice's first side, then every second side, and fill the pan 2 sides at a time. Could both sides of one slice land in the same round?
Worked solution
Have a go first, then read the solution step by step.
1.6 slices have 6 first sides and 6 second sides: 6 × 2 = 12 sides to fry.
2.Each round fries at most 2 sides: 12 ÷ 2 = 6, so at least 6 rounds.
3.6 rounds can be done: list the first sides of slices 1 to 6, then the second sides of slices 1 to 6, and fry them 2 at a time from the front. A slice's two sides are 6 places apart, more than 2, so never in the same round, and the first side always comes first.
4.So the fewest is 6 × 6 = 36 minutes.
⚠️Common mistake: forgetting each slice has two sides, counting only 6, and answering 18 minutes.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download