Question 58
The set $\{1, 2, \ldots, 10\}$ is split to three parts. For each part 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 the first part has the largest sum of elements, the second part has the largest product of elements, and the third part has the largest sum of digits?
Is it possible that the first part has the largest sum of elements, the second part has the largest product of elements, and the third part has the largest sum of digits?