Find the smallest positive integer that is a multiple of 35 whose digits are all the same.
Since this puzzle corresponds to a particular case of my "Sevens And Zeroes Problem" ( http://perplexus.info/show.php?pid=4348); 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