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Another math puzzle

Here’s a cool math trick I saw once.

The number 789789 is a multiple of 13.  789789 = 60573 * 13
The number 123123 is also a multiple 13.  123123 = 9471 * 13
Assertion: Any number of the form ABCABC is a multiple of 13.

The assertion is true.  I can prove it.  Can you?

This entry was posted on Tuesday, June 20th, 2006 at 12:34 pm and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “Another math puzzle”

  1. R.Kesavan Says:
    August 4th, 2006 at 3:42 am

    Any number of the form ABCABC is not only divisible by 13, but also by 11 and 7. Here is the proof:
    ABCABC= ABC000+ABC
    = ABC(1000)+ABC
    = ABC(1000+1)
    =ABC(1001)
    =ABC(13X11X7) (because 1001 is a product of 7,11,and 13.

    Q.E.D.

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