Dozens poster
Dozens Poster
Age
11 to 14
Challenge level
Problem
Student Solutions
54312
Why?
It must be a multiple of 3
1 + 3 + 4 + 5 = 13 so the remaining digit could be 2, 5, 8
Try 8. It must be a multiple of 4 so the last two digits must be divisible by 4.
85314
2-digit multiples of 4 which end in 4 (or 8) have second-last digit even: 04, 24, 44, 64, 84
Best option with 8: 53184
Try 5: impossible since we can't make a multiple of 4
Try 2.
Using previous pattern, 53124
But 2-digit multiples of 4 which end in 2 have second-last digit odd: 12, 32, 52, ...
54312
This is the largest possibility