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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

Best Answer 

 #3
avatar+26329 
+15

Here's a proof that only the three digits 1, 2 and 3 are involved:

 

 Digits

.

Alan  Jul 11, 2015
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4+0 Answers

 #1
avatar+78755 
+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
avatar+91051 
+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
 #3
avatar+26329 
+15
Best Answer

Here's a proof that only the three digits 1, 2 and 3 are involved:

 

 Digits

.

Alan  Jul 11, 2015
 #4
avatar+91051 
+5

Thanks Alan, that is great   

Melody  Jul 11, 2015

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