A medium question on most and least for P2–P4, 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
There are 4 digit cards:
0, 5, 7, 8.
3 of them make a three-digit number, each card used once, and 0 can't go first.
Of the three-digit numbers that can be made, how much bigger is the biggest odd one than the smallest even one?
Show the hints (2)
💡Hint 1: Which place decides whether a number is odd or even? First think which cards can go in the units place.
💡Hint 2: Once the units digit is fixed: for the biggest, put the rest in decreasing order; for the smallest, lead with the smallest non-zero digit, then increasing. Try every card that can go in the units place.
Worked solution
Have a go first, then read the solution step by step.
1.Biggest odd: the units digit can be 5 or 7, the other cards in decreasing order. units 5 → 875; units 7 → 857. The biggest is 875.
2.Smallest even: the units digit can be 0 or 8; lead with the smallest non-zero digit, then increasing. units 0 → 570; units 8 → 508. The smallest is 508.
3.The difference: 875 − 508 = 367.
⚠️Common mistake: trying only one possible units digit, or putting 0 first (057 isn't a three-digit number).
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