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Three Digit Trial (Posted on 2014-05-07) Difficulty: 2 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Solution answer Comment 1 of 1

The 3-digit number must be a palyndrome, say  a string aba.

2a+b=ab  (eq 1))

 Yields       b=2a/(a-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
  Posted by Ady TZIDON on 2014-05-07 09:49:39

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