Here is another entertaining problem with the nine digits, the nought
being excluded. Using each figure once, and only once, we can form two
multiplication sums that have the same product, and this may be done in
many ways. For example, 7 × 658 and 14 × 329 contain all the digits
once, and the product in each case is the same--4,606. Now, it will be
seen that the sum of the digits in the product is 16, which is neither
the highest nor the lowest sum so obtainable. Can you find the solution
of the problem that gives the lowest possible sum of digits in the
common product? Also that which gives the highest possible sum?