Using each of the 10 digits once, find two 5-digit numbers with the smallest possible product.

Answer 1

Assuming the first digit can't be 0, you start with first digits of 1 and 2; then, at each place, note that you get a lower product by having the lowest remaining value with the 1; then note that, looking at the remaining values, you get the lowest product by assigning the next lowest value to the 2 at that place. Thus, you take the product of 10468 and 23579