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Number = Sum (Digit)*Product (Digit) (Posted on 2010-06-21) Difficulty: 2 of 5
N is a positive base ten integer having at least 2-digits but at most 4-digits, which is obtained by multiplying the sum of its digits with the product of its digits. It is known that N cannot contain any leading zero.

Determine all possible value(s) of N.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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this 'N that | Comment 9 of 10 |
(In reply to re: No Subject by Charlie)

Your point is well taken, Charlie; "its" requires a singular antecedent, rather than the collective set of digits as such -- so "N" is that antecedent (a string of two to four digits of which the first is not zero).  Is the second sentence ("It is known that N cannot contain any LEADING zero.") otiose and just intended to mislead?  Clearly if ANY of the digits of N were zero, then the product would be zero, so there would be no solution. So, all in all, ad astra... 
  Posted by ed bottemiller on 2010-06-22 12:55:01

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