MathDB

The set

\{1, 2, . . . , 10\}

is partitioned to three subsets

A, B

and

C.

For each subset the sum of its elements, the product of its elements and the sum of the digits of all its elements are calculated. Is it possible that

A

alone has the largest sum of elements,

B

alone has the largest product of elements, and

C

alone has the largest sum of digits?

Problem Statement