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35, 70, 105, 140... (Posted on 2006-05-03) Difficulty: 2 of 5
Find the smallest positive integer that is a multiple of 35 whose digits are all the same.

See The Solution Submitted by Rob    
Rating: 3.0000 (4 votes)

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Hints/Tips Some Tips | Comment 1 of 8

Since this puzzle corresponds to a particular case of my "Sevens And Zeroes Problem" (; I underline herewith some salient hints towards a solution of this problem.<o:p></o:p>

(i) Consider that 35=5*7.<o:p></o:p>

(ii) This allows for repetitition of only one digit in terms of the problem.<o:p></o:p>

(iii) Think about the divisibility of 7 and  the associated numbers. This will immediately lead to the solution.  

Edited on May 3, 2006, 9:35 am
  Posted by K Sengupta on 2006-05-03 09:34:58

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