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Ring in 2013 (Posted on 2012-12-31) Difficulty: 3 of 5
Start as you wish had you prove that for any k-digit number M there exists a number n such that the string of first k digits of 2n equals M.

Find a power of 2 whose decimal expansion begins with the 12-digit string "201320132013". It need not be the smallest such number.

Bonus: Find the smallest such number and prove it to be the smallest.

See The Solution Submitted by Charlie    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re(3): 'Slide Rule' Logic | Comment 4 of 5 |
(In reply to re(2): 'Slide Rule' Logic by broll)

Yes, logarithms are needed for the terribly huge numbers involved, as well as extended precision arithmetic.

But it could be handled manually in a few steps given an available log function in extended precision calculator software.

Edited on January 2, 2013, 12:10 pm
  Posted by Charlie on 2013-01-02 12:09:36

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