perplexus.info :: Just Math : Move the 2

Move the 2 - double the number II (Posted on 2011-08-21)

(I) A certain tridecimal (base 13) positive integer starts with the digit 2. Moving the 2 from the beginning of the number to its end doubles it.

What is the minimum value of this number?

(II) Determine the general form of a positive integer n such that there does not exist any base-n positive integer, starting with the digit 2, that doubles itself when the digit 2 is shifted from the beginning of the number to its end.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(I) The required minimum value of the number is 2495BA8371.
For an explanation, refer to the solution submitted by Charlie in this location.
(II) The bases that do not work are those that equal 2 mod 4. Any other base will have a solution.
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
computer exploration of part II (likely spoiler)	Charlie	2011-08-21 14:12:13
Part I solution	Charlie	2011-08-21 13:47:32

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