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Discussion of Problem 1407. One-two, One-two

HINT
Posted by hoan 26 Dec 2010 22:03
prove that for any n, exist number only whit 1 and 2 digit and have n digit that divided by 2^n.
like this:
n=1 -> 2
n=2 -> 12
n=3 -> 112
n=4 -> 2112
.
.
.

sorry for my poor english.
GOOD LUCK!!!