A number has three distinct digits. The sum of the digits equals the product of the digits. How many three-digit numbers satisfy this condition?

Dabae
Jul 7, 2015

#1**+10 **

I believe this might be all the permutations of the divisors of the perfect number, "6"

Note 1 + 2 + 3 = 6 = 1* 2 *3 so...the three digit numbers are

123, 132, 213, 231 312, 321

CPhill
Jul 7, 2015

#2**+5 **

Thanks Chris,

Mmm I can't think of any others either but I would like to see a proof or a concrete demonstration that there are no others.

Melody
Jul 11, 2015