There are 362,880 different numbers that use the digits 1 to 9 exactly once (like 187,432,569).

Of these, what percentage are prime numbers?

None, a way to check if a number is divisible by three is to add up the digits in the number to see if the result is divisible by three.
i.e.

192--->1+9+2=12 and 12 is divisible by three; check it, 192/3=64.

So, 1+2+3+4+5+6+7+8+9=45 and 45 is divisible by three. No matter the order of the digits in the larger number they will all be divisible by three, and therefore none are prime numbers.

I guess a better solution involves a proof of this assumption about #'s divisible by three.

Posted by Nick Murray on 2002-12-17 02:57:24