A certain number ends with the digit 2. Moving the 2 from the end of the number to its front doubles it. Can you find this number?

(Hint: it's quite large)

This can be approached as a division problem, and thereby proceed from left to right, and it seems as easy as the multiplication approach:

  1


2)2

so place a 1 to the right in the dividend:

  1


2)21


  2 


  01

requiring a zero in the quotient, and also to the right in the dividend, and brought down:

  10


2)210


  2 


  010

leading to a 5 in the quotient and dividend:

  105


2)2105


  2 


  010


   10


    05

leading to a 2, etc.

until eventually a 04 (not a 05) appears at the bottom that has to be divided by 2, so a 2 can be placed at the rightmost portion and zero out the bottom subtraction.

Posted by Charlie on 2003-06-04 04:01:16