See if you can...

Good luck. wink

oooh..that's weird.... eek!

Indeed, but one must make sure he follows the directions EXACTLY, or, like my mother, you'll claim the guy is wrong all the time. (She still can't figure out where she messed up.)

I kind of figured it out.

When you subtract 2 numbers that have the same digits in different order, the resulting number is always a multiple of 9, which means that its digits added together are also a multiple of 9.

For example, 315 - 153 = 162 which is 18 x 9. And 1 + 6 + 2 = 9.

So when you pick 1 of the digits and enter the remaining ones, the program can easily figure out the number you circled.

Interesting, if this is, indeed, the explanation.

HAHAHH. Of course it is. It's nice to know that my number theory class in college didn't go to waste.

wwcd is correct. i love numbers...

Aren't many of these number things related to our use of a base 10 system?

OK, in layman's terms, here's an explanation:

THEOREM. Take any number X; jumble up its digits to get Y; subtract the lesser from the greater of X and Y; the answer is bound to be divisible by 9.

PROOF. Suppose the digits of the original number, in order, are A, B, C, D,... That means that the number is A times some power of ten, plus B times the next-lower power of ten, plus C times the next-lower power of ten, and so on. When you jumble up the digits to make a new number, this new number will **still** be A times some power of ten, plus B times some power of ten, plus... Only the powers are different! Subtracting gives you A times (some power of ten minus some other power of ten) plus B times (some power of ten minus some other power of ten) plus... But any power of ten minus any other power of ten gives you a number divisible by nine. ( E.g. 10,000 minus 10 gives you 9,990.) So the result of your subtraction must divide by 9.

So that 4-digit difference -- the result of your subtraction in step 2 of the dog puzzle -- is bound to be some multiple of 9. For illustration, I'll suppose it's 7524, which does indeed divide by 9.

Instead of removing your chosen digit D (I'll choose D=5) from that difference, just imagine replacing the digit D by a zero. Call the resulting 4-digit number N. In my example, N=7024.

Now, treat that final step--jumbling the three remaining digits--as jumbling up the **four** digits of N, but making sure the zero ends up at far left. (E.g. treat jumbling up 724 to get 247 as jumbling up N=7024 to get 0247.)

By my theorem, the 3-digit (ignoring the leading zero now) result of this jumble differs from N by some multiple of 9. (Yes it does: 7024 minus 247 equals 6777, which is 9 times 753.)

AND, it also differs by some multiple of 9 from the number you get if you jumble up N's digits to put the zero -- the one that replaced the mystery digit -- at the far right, units, position. So 247 doesn't just differ from 7024 by some multiple of 9, but also from 7420 likewise... which is some multiple of 9, minus D! (Yep: 247 differs from 7420 by 7173, which is 9 times 797. and 7420 is 9 times 825, minus 5.)

Armed with this understanding, divide that final, jumbled, 3-digit number by 9 and note the remainder R. R, plus the mystery digit D, must equal 9. So D is 9 minus R. (247 is 9 times 27, remainder 4. 4 plus 5 is 9.)

So all the dog program does is look at your final, jumbled-up three digits, divide by 9 to get the remainder, and subtract that remainder form 9. Note that the final, jumbled-up three digits can't divide EXACTLY by 9 (giving remainder zero), because then so would my "N," which would mean you hadn't removed a digit....

from Judy:
Wow Judgie, now you're even making up your own mathematical theorems. I'm so impressed!

I made up nothing, child. Obviously math wasn't one of your strongest subjects. No surprise there.

Well if you consider 800 out of 800 on the SAT "not strong", then sure. But I stand corrected, you didn't make anything up....you just copied it from someone else.

[ March 01, 2006, 07:43 AM: Message edited by: HotlantaTarheel ]

Now girls. No fighting.

MIB, I thought you were asking because you didn't know how it worked! I didn't realize it was a test.

And, you really shouldn't use the phrase "in layman's terms." Comes off a little snotty.

He didn't know how it worked, but of course he will claim he did. He'll probably even claim that he created the whole thing just to test us.

I didn't know exactly how it worked, even though I knew there was a mathematical explanation.

It wasn't meant as a test, either. I got the link to that thing in an Email a friend of mine sent me. He also sent the explanation in a separate Email but suggested I not read it right away, so I left that in my in-box without reading it, so as to not spoil the fun, so to speak.

I'm sure that my buddy got the thing from somewhere else--where I don't know. You know how these Internet jokes and Internet puzzle things make their way around.

It shouldn't surprise me that Hotlanta had to come in here and throw cold water over the whole thing, as he usually does. His comments were really unnecessary, since this whole thread was just one meant for a little fun. Alas, left-wing nutjobs like him tend not to enjoy the little fun things in life.

I did that intentionally. I thought even you would be able to detect the sarcasm there. wink

[ March 01, 2006, 08:37 AM: Message edited by: MIB ]

Uhhh...Judy you were the one that said to me:
Its obvious you were purposefully trying to put me down because I alluded to the fact that you just copied someone else's explanation and posted it as your own.

and: I prefer the term Socialist, but lets keep that to the Politics thread.

Ah, the devil has been revealed. Aye, Comrade lenin!

No Judy, Lenin was a communist.

http://en.wikipedia.org/wiki/Christian_socialism

Uh, no. Lenin was the Socialist, Stalin the Communist. Do you not remember the Bolshevik revolution? Obviously you didn't do as well in History as you did in math.

Impressive.

I did very well in math in school, having taken subjects all the way up to Honors Calculus in high school. That was the highest level course offered in anything math-related at our school.

I did well in math; but I hated it. I still do. For some reason I put up this big anti-math shield whenever I have to tackle math-related problems. Most people who did well in math would probably have the opposite attitude. Not me. For some strange reason, even though I did well in it, I can't stand it.

It's too bad so many kids nowadays do very poorly in it.

Actually, the October Revolution, as it was called, was led by 3 forces. The Bolsheviks, (which were the largest), the Mensheveks, and the Communists. It was only after Lenin died, (or was murdered by Stalin as some think), that the Bolshevik/Communist takeover was complete.

Stalin ensured this by the murder of Trotsky, who was living in Mexico City at the time of his death.

Indeed.

Things in Russia started off as this nice, little Socialist takeover and eventually led to an oppressive Communist regime.

I always did find it rather amusing that the Soviet Union was a communist country when its very name, the USSR, implied it was socialist.

Oh well, back to this thread's stupid little math game.

I find computational mathematics fun; theoretical math, however, is for the birds...in college, math soon involved more words than numbers, so I got out quickly...comp sci became my major and a lowly minor in math.