Which 5 numbers that have a mean of 10 and a median of 12?

Answer 1

There are infinitely many sets.

Restricting the answers to positive integers, you can have

1, 1, 12, 13, 23;

1, 1, 12, 14, 22;

1, 1, 12, 15, 21;

and so on until

1, 1, 12, 18, 18.

Then you go to 1, 2, 12, 13, 22 and so on.

Perhaps you can now see that there are very many possible solutions. And the number of solutions increases if negative integers are permitted. And increases to infinitely many if real numbers are permitted instead of only integers.