Question

How many distinct sets of three positive integers have a mean of $6,a$ median of $7$, and no mode?

Answer 1

Mean$=6$

$\therefore$ Sum$=6\times 3=18$

Median$=7$

It must be the numbers less than $7$ and greater than $7$ and $7$ must be included.

Examples:$\{1,7,10\}$

$\{2,7,9\}$ and $\{3,7,8\}$

So there are three sets.