(a) Find two positive integers, N1 and N2, such that for each:
* the sum of digits of the integer equals the product of digits of its square root, and
* the digit '1' does not appear in either the original integer or its square root.

(b) Can you find any others?

(c) Can you explain why there would be so many more solutions if we allowed the digit '1' to appear?

Use of 1's allows the products in the square roots not to get too big too fast so as to overwhelm the sums in the numbers. 

Posted by Charlie on 2023-02-09 09:34:45