Originally posted by: goku
doood! Though, if you were to take 111, scramble the numbers and subtract the difference, you'd end up with 0 and that's no divisible by 9..
Originally posted by: JujuFish
Originally posted by: goku
doood! Though, if you were to take 111, scramble the numbers and subtract the difference, you'd end up with 0 and that's no divisible by 9..
You fail at math.
Originally posted by: goku
Originally posted by: JujuFish
Originally posted by: goku
doood! Though, if you were to take 111, scramble the numbers and subtract the difference, you'd end up with 0 and that's no divisible by 9..
You fail at math.
You fail at proving people wrong. 111-111=0 0/9=0
Originally posted by: tom3
This works because of the following:
The value of the number ABCDE (where each letter is a digit) is 10000*A + 1000*B + 100*C + 10*D + 1*E. If we look at just one of the digits and the value it contributes to the sum, let's say, B, which contributes 1000*B to the sum in this case. And we test out all the possible positions it may end up, we have B####, #B###, ##B##, ###B#, ####B; contributing 10000*B, 1000*B, 100*B, 10*B, a*B respectively.
Now if you take the difference between these 5 possible values and 1000*B (from the original number), you get 9000*B, 0*B, 900*B, 990*B, 999*B respectively, all of which are B multiplied by a multiple of 9. Now if the contributed value difference for each of the digits before and after scrambling is always a multiple of 9, then the sum will always be a multiple of 9.
Originally posted by: blueshoe
HOW does this work??
Originally posted by: blueshoe
Select any number with at least 2 digits (12345 for example).
Scramble the numbers. (34125)
Take the difference.
The difference will always be a multiple of 9. :Q
HOW does this work??
Originally posted by: QED
Originally posted by: blueshoe
HOW does this work??
It works because of simple modular arithimetic, and actually works for numbers of any length.
Modular arithithemetic, greatly simplified, is simply considering only the remainder of a number when divided by some fixed integer, say 9.
For instance, we say 1 is congruent to 10 modulo 9 because both 1 and 10 leave a remainder of 1 when divided by 9. Obviously, if a number is congruent to 0 modulo 9 then it must be divisible by 9.
A lot of the laws and rules that work for equations in regular algebra also hold for congruencies in modular arithemetic. If x is congruent to y modulo 9, then n*x is also congruent to n*y modulo 9.
Now consider a 4 digit number abcd: it can be written as 1000a + 100b + 10c + d, where a,b,c,d are integers between 0 and 9.
Now we know that 1000 is congruent to 1 modulo 9, so 1000a is congruent to 1*a modulo 9.
100 is also congruent to 1 modulo 9, so 100b is congruent to 1*b modulo 9.
10 is congruent to 1 modulo 9, so 10c is congruent to 1*c modulo 9.
Hence, 1000a + 100b + 10c + d is congruent to 1*a + 1*b + 1*c + d, or (a+b+c+d), modulo 9. In other words, the number is congruent to the sum of its digits, modulo 9.
Notice that this equivalancy is not dependent anymore on the positions of the digits a, b, c, or d within the number. If you switch the digits around, their sum is still the same.
Hence, the difference between two 4-digit numbers using the same set of digits is congruent to the difference between the sum of those digits and the sum of those digits modulo 9 (i.e. 0). But when a number is congruent to 0 modulo 9, that means it is divisible by 9-- so the difference between the two digits numbers is divisible by 9.
Originally posted by: LoKe
Basically, it works because of the rocksalt effect. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Nam condimentum, nibh a ullamcorper rhoncus, lectus metus consectetuer odio, id suscipit libero massa aliquet arcu. Praesent mattis, nisl a aliquet faucibus, mauris purus imperdiet enim, a vestibulum urna turpis eu sem. Donec ornare mauris sit amet justo. Donec vestibulum auctor enim. Integer placerat dolor ac risus. Fusce tempor scelerisque sapien. Suspendisse elit. Nulla facilisi. In id nisi interdum orci accumsan tempus. Phasellus tincidunt. Aliquam placerat pede ac massa. Curabitur pretium tristique velit. Aliquam eget risus ac eros faucibus consectetuer. Sed eleifend ipsum eu ante. Ut ut turpis in orci ornare congue.
Suspendisse et nunc eu eros consequat volutpat. Nullam id lacus quis sapien ornare fringilla. Curabitur posuere urna eu metus. Fusce vitae lectus. Duis ut leo sed lacus dictum lobortis. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Sed leo. Aenean gravida bibendum lectus. Donec auctor elit venenatis erat. Pellentesque eu urna. Suspendisse semper blandit purus. Maecenas cursus, lacus non semper cursus, nisi neque viverra velit, non venenatis lacus felis ut urna. This is just to throw you off and make you think I'm smart. Because I'm not.Vestibulum ut metus vel nisi congue tincidunt. In placerat. Duis ante nulla, tincidunt in, fermentum a, sollicitudin sed, nulla.
Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Donec turpis mauris, porta non, malesuada sit amet, lacinia vel, massa. Class aptent taciti sociosqu ad litora torquent per conubia nostra, 9000^B, blah blah blah, per inceptos hymenaeos. Quisque laoreet consectetuer nibh. Donec quis pede ac diam viverra nonummy. Aliquam vulputate euismod erat. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Sed sodales. Sed risus mauris, dignissim quis, malesuada a, pharetra a, augue.