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Cute numbers (Posted on 2016-07-21) Difficulty: 2 of 5
39=3*9+3+9
Is it not cute?
Let's attach the adjective cute to all numbers equaling the sum of their digit augmented by the digits' product.

List all the cute numbers below 100.

Are there cute numbers bigger thann 100?

No Solution Yet Submitted by Ady TZIDON    
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short review | Comment 2 of 5 |

10a+b=ab+a+b, from which 10a = ab+a, and 10=b+1; and 10a=9a+a, which is true for any a.

For numbers over 100, cute is not well-defined. For example a could be larger than 10, in which case there would be many solutions.

If the idea is that 100a+10b+c = abc+a+b+c, then there are no solutions with a,b,c, all positive and less than 10.


  Posted by broll on 2016-07-21 23:16:01
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