Difference between revisions of "1997 AIME Problems"

(Problem 7)
(Problem 7: the problem listed here belongs to the 1999 AIME not the 1997 AIME)
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== Problem 7 ==
 
== Problem 7 ==
There is a set of 1000 switches, each of which has four positions, called <math>A, B, C</math>, and <math>D</math>.  When the position of any switch changes, it is only from <math>A</math> to <math>B</math>, from <math>B</math> to <math>C</math>, from <math>C</math> to <math>D</math>, or from <math>D</math> to <math>A</math>.  Initially each switch is in position <math>A</math>.  The switches are labeled with the 1000 different integers <math>(2^{x})(3^{y})(5^{z})</math>, where <math>x, y</math>, and <math>z</math> take on the values <math>0, 1, \ldots, 9</math>.  At step i of a 1000-step process, the <math>i</math>-th switch is advanced one step, and so are all the other switches whose labels divide the label on the <math>i</math>-th switch.  After step 1000 has been completed, how many switches will be in position <math>A</math>?
 
 
  
 
[[1997 AIME Problems/Problem 7|Solution]]
 
[[1997 AIME Problems/Problem 7|Solution]]

Revision as of 18:22, 12 August 2006

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