OK. I'll admit I'm procrastinating at my desk, posting this instead of doing work. But I justify it by saying I'm adding to human enjoyment throughout the universe, and that is much more important than my job.

When most of us went to school, we were taught simple divisibility rules. For example, if a number is even, we can divide it by 2. If the sum of the digits is divisible by 3, the number is divisible by 3. If it ends in 0 or 5, it is divisible by 5, etc. But the divisibility rule for 7 is rarely taught. And unless you take a university level number theory course, you may never learn it. (hang with me and you'll see how this applies to 17) The rule for 7 goes like this:

Take any number. Cut off the last digit. Multiply that cut digit by 2 and subtract it from the remaining number. If the result is divisible by 7, the number is divisible by 7. As an example, take the number 861. To test for 7, we first cut the last digit [1], leaving us with the number 86. We then subtract twice the digit we cut [1], yielding 86 - 2 x 1 = 84. And since we all still remember our 12 times tables, we immediately know 84 = 12x7. If not, we could just do it again. (Cut 4, leaving 8, subtract 2x4 = 8 from 8, leaving 0, and zero is divisible by 7)

So that's 7, but what about 17? Well, it turns out that this trick comes directly from a whole family of tricks involving the Diophantine equation (10x + N + 1) mod(N) = 0. You can check it for 7, with x = 2, N = 7

(10 x 2 + 7 + 1) = (20 + 7 + 1) = 28 mod(7) = 0.

• (mod(N) is just a fancy way of saying "remainder". So 13 mod(5) = 3. (5x2+3 = 13) 19 mod(3) = 1. (6x3+1 = 19) *

Now I can explain why I like 17.

The multiplier (x) to make this trick work for 7, turns out to be 2, the easiest possible multiplier. Most people can easily double a single digit number in their heads. But the second simplest value that most people can easily do is 5. And guess what the multiplier is for 17? Yep. 5. (10x5+17+1 = 68 = 17x4)!

So knowing this little trick and just a few multiples of 17, you can easily look for congruences of 17 in all the numbers you encounter throughout the day. Does your bill come out to $8.84? Well, you see 884, cut off the 4 leaving 88, then subtract 4x5. Leaving 68. But 68 is 4x17. The universe just showed you a 17 and you probably didn't even realize it. Driving and notice the license plate in front of you is 391? You guessed it. That's also a 17. (39-5x1 = 34 = 17x2) Start doing this everyday and you will be amazed how often the number 17 actually comes up in your life. For me, it seems to appear far more often than random chance would suggest.

And if nothing else, at least it's a fun trick to impress your friends with at parties.