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5 unknown digits (Posted on 2014-05-13) Difficulty: 4 of 5
Each of the three consecutive 3-digit numbers n, n+1, n+2 divides N=146,8XX,XXX, where each X represents a digit below 6 .

Please restore N,n.

See The Solution Submitted by Ady TZIDON    
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Solution Solution | Comment 1 of 5
I originally made the mistake of assuming the three numbers were relatively prime and that N has to be a multiple of their product.  (In that case the first 3 digit solution is n=123 and 123*124*125*77 = 1468900500.)

However if n is even then N need only be a multiple of half their product.   The solution comes from the first number we can try:
100*101*102/2*285 = 146803500.

The first was basically a brute force solution using Excel.  The second one didn't need to be but was a simple change.

Edited on May 13, 2014, 3:43 pm
  Posted by Jer on 2014-05-13 13:41:40

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