Shane Hathaway shane at
Fri Nov 20 13:13:44 MST 2009

Sasha Pachev wrote:
> I just came up with this while teaching my son about numbers. Let's
> see how quickly somebody figures this out.
> If you had a 64 bit number written down in hex, how could you quickly
> tell without the aid of any computational device, including pencil or
> paper if it is divisible by 15?

The 9's rule in decimal becomes the 15's rule in hexadecimal.  Add the 
digits together in hex, then add those digits again, until you get a 
single digit.  If the single digit is F, then it's divisible by 15.

> How about 17?

Two-digit representations of multiples of 17 are easy enough, but more 
digits aren't obvious.  I'd look to rows in Pascal's triangle for powers 
of 17.


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