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))
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