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8s and 9s (Posted on 2011-12-21) Difficulty: 3 of 5
Find a 13 digit positive integer N whose base ten representation consists entirely of 8s and 9s such that 213 divides N.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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answers- spoiler | Comment 2 of 7 |

8,898,989,989,888

it is easy to build up from 8, 88, 888, 9888 etc by adding an 8 or 9 (depending on the parity of the prev/2^n )in front of the previous string of 8s &9s .

proof: by induction.

Edited on December 22, 2011, 11:00 am
  Posted by Ady TZIDON on 2011-12-21 12:14:35

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