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?

(In reply to re: simple guess by TomM)

The way I think about it is: Start with 9=9, Each time you add 9, you are just adding 1 to the tens place and subtracting 1 from the ones place. Once you get 99 (or 97, another like number), you just subtract 1 from the ones place and add 1 to the hundreds place, and make the other number(s) (which should be 9) 0.

So, you have either added a net amount of 9,0,-9 each time. This means the sum of the digits will be a multiple of 9.

This is the same idea with the divisible by 3 idea. You are adding a net amount of 9, 6, 3, 0, -3, -6, -9...

Posted by Gamer on 2003-04-26 12:16:42