Find a 3-digit positive integer N such that the sum of the three digits of N equals the product of the first two digits of N and also equals the product of the last two digits of N.

How many values of N are there? Prove that there are no others.

*** N does not contain any leading zero.

The 3-digit number must be a palyndrome, say a string **aba**.

**2a+b=ab **(eq 1))

Yields **b=2a/(a-1**)

With integer solutions **( a,b) = (2,4) & ( a,b) = (3,3) **

Answer: **242 **&** 333**.

The disclaimer re leading zeroes is **immaterial** and therefore redundant: although 000 might fit the eq 1, it cannot qualify as a 3 digit number.

*Edited on ***May 7, 2014, 9:59 am**