Okay, I know this probably has a perfectly simple and logical mathematical answer, but I’ve always been lousy at figuring out number puzzles. My co-workers are no better (one co-worker, in fact, hid her paper from the screen, so the little 7 Up guy couldn’t peek at it). So can someone smarter than me tell me how this thing works?
My guess is it has something to do with the magic number 9.
But I still can’t see how. Boy, that’s a clever maths trick!
Groovey
How’s your algebra? You’ll need it for this site, which explains it pretty well, I think.
Yeah, it’s all done with 9s. 
Just like that Crystal Ball site that had everybody on boards other than this one so puzzled. 
Do you remembe the test for divisiblity by 9? You sum the digits. Then sum the digits of the result until you have a single digit. If the result is 9, the number is divisible by 9. If the result is not 9, then the result is the remainder you get if you divide the original number by 9.
Rearanging the digits does not change the remainder. Let r be the remainder. The original number is 9k[sub]1[/sub] + r, for some k[sub]1[/sub]. When you rearange the digits, the number is going to be 9k[sub]2[/sub], for some k[sub]2[/sub]. The difference is 9(k[sub]1[/sub] - k[sub]2[/sub]) (or its negative). Since we have a multiple of 9 now, we know that the sum of the digits of the difference must be 9. We can use this to find the missing digit. Sum the remaining digits until you have a single digit. If you get 9, the missing digit must be 9. If the sum is not 9, subtract the result from 9 and you will have the missing digit.
The reason they asked you not to circle a zero is this process cannot distinguish a zero from a nine.
I figured it probably had something to do with 9s, but I’m still not clear on how this one works. Mikie’s site is kind of sort of penetrating the fog, but it’s the random bit at the end where it has you circle a number and then shows you the number you circled that has me confused.
What kills me is the answer is probably staring me right in the face and I’ll have to hit myself in the head and say, “D’oh!” as soon as someone points it out to me. My defense is I’m on Darvocet for back pain.
preview
reads DrMatrix’s explanation
D’oh! :smack:
Thanks, guys!
I love the instruction to “make it completely random, with lots of different digits.”
Very sneaky. A completely random number might have all the same digits, but if you did that, then rearrange the digits and subtract, you’d get 0 and the trick wouldn’t work.
The above should be:
When you rearange the digits, the number is going to be 9k[sub]2[/sub] + r, for some k[sub]2[/sub].
Sorry for this slight hijack. It says Moderator under your name, so doesn’t that mean you “…generally have the ability to edit and delete posts…” (direct quote from the board’s faq) including your own? Or is that “generally” implying that only some mods can do that?
Perhaps Moderators are discouraged from using their powers to just fix typos ad things.
The puzzle doesn’t work if you choose 666 as your starting number. I guess the devil is in the details.
They ask for different numbers. You can’t subtract the same number from itself, that just wouldn’t work.
It didn’t work with 1111 either (my first try). Oh. I see you’ve alteady noticed that. I’m posting anyway. It’s been a while.
I could have edited my post for the correction, but I was posting as a member, not as a moderator. Since members cannot edit their posts, it’s not really fair for me to edit my posts when I’m posting as a member.
There is no official rule about this, and if I’d noticed the mistake right away, I might have edited it for the correction (and corrected my mis-spelling of remember).