3

Part of 2015 Canadian Mathematical Olympiad Qualification

Problems(1)

Mediocre numbers

Source: Canada Repêchage 2015/3

N

be a 3-digit number with three distinct non-zero digits. We say that

N

is mediocre if it has the property that when all six 3-digit permutations of

N

are written down, the average is

N

N = 481

is mediocre, since it is the average of

\{418, 481, 148, 184, 814, 841\}

.
Determine the largest mediocre number.

number theorypermutationsAverage