Problem 58977. Find the smallest number leading to a maximal product of two numbers that concatenate to another number
Cody Problem 58971 involves the maximal product of numbers that concatenate to a number n. For example, if , then the products are , , and , and the maximal product is 492. For , the maximal product is zero.
This problem seeks the smallest number leading to a given maximal product. If the product is 492, the smallest number is 682. Some products have no solution. For example, 13 is a product of both 113 and 131, but the maximal products are 33 and 31, respectively.
Write a function that takes a maximal product and returns the smallest number leading to that product. If the product has no corresponding number, return the empty set.
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