imanerd
So last night I got an email from my Aunt Cro, giving me a link to a website for 7-up, where there is this number-guessing game. What happens is, you pick a number with 3 or more digits, then rearrange the digits and subtract that number from the first one (ex: 7654-5746=1908). Then you take that new number (1908) and circle one of the digits
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I take that as a challenge. This is a tough one, though. Or maybe it's one of those problems that seems impossible at first, but when you see the solution, you're thinking, "oh, duh!"
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One rule that I forgot to mention was, the number you pick can't be a zero. Bonus points for if you can figure out why you can't pick zero. I did.
Oh, and if you want to see the game in action, you can find it at: www.digicc.com/fido/
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Every answer that results from finding the difference between a number and its scrambled version (as long as it's 3 digits or more) is divisible by 9. And it just so happens that when a number is divisible by 9, it doesn't matter what order you put the digits in, it's always divisible by 9.
So, the applet takes the numbers you give it, starts dividing by 9, and when it gets a remainder, it finds what digit can be added to make the number cleanly divide. For example, if the remainder is 4, then adding a 5 to the dividend will make it divide cleanly by 9. This is the digit you circled and pulled out.
So that's what it does. As to why it works, I didn't figure that out, i.e. why are multiples of 9 able to be rearranged and still be a multiple of 9. Obviously, if you circle a zero, then the number returned will always be a 9, because that's the only digit you can add to zero to make it work. As to why it has to be a three-digit-or-more number to start with, I didn't figure that out either.
Let me know if there's more to it.
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I dont think it does hafta be three digits.
PS: Derrick sucks.
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