369

[Awani]

I dabbled a bit in this before and I found it interesting that the following pattern always emerge...

If you take any number, lets say 418 and then add up all its combinations like:

418
814
148
184
481
841

Total = 2886 = 2+8+8+6 = 6

Now you do the same with 417 = 9, 416 = 3, 415 = 6, 414 = 9 etc...

The pattern is always 3, 6, 9... magic numbers.

Nothing new, but interesting!

[Zephyr]

Most curious. At what point does this pattern begin? As soon as the 10 basic digits are exhausted?
11+11=22-->4
12+21=33-->6
13+31=44-->8
14+41=55-->10-->1
...
25+52=77-->14-->5
...
56+65=121-->4
...
98+89=187-->16-->7
99+99=198-->18-->9
.
100+010+001=111-->3
101+101+110+110+011+011=444-->12-->3
102+201+120+210+021+012=666-->18-->9
...

Well, it looks like the crunched sums of single digits go up in increments of one, in two digit, they go up in increments of two, and in three, they would go up in increments of 3. Howevever we see that "101" and "102" are a counterexample to this pattern. I wonder why?

*Zephyr*

[LeoRetilus]

Interesting, sometimes I find myself with a calculator in my hand and find simliar patterns, except I always find myself multipying 9 times other numbers and resolving the sum back to nine.

For example: 9x9x6x7=3402 -> 3+4+0+2=9
9x4x5x3x9x5=24300 ->2+4+3+0+0=9
6x9x21x15x3=51030 ->5+1+0+3+0=9
and on and on , but it does stop at one point then begin again

The magical number 9

[Ghislain]

All multiples of nine resolve back to nine.

It is the principle whereby you predict what
a person is going to say.

Try this on someone:

• tell them to pick a number
• now multiply the number by nine
• if the resulting number has more than one digit
  keep adding the digits together until it resolves
  to one digit (which you know will be nine)
• get them to subtract 5 from their total
  (they now have four)
• tell them to associate the number with a letter
  from the alphabet (a=1,b=2.....) they now have
  "d"
• tell them to choose a country (in english) starting
  with their letter. It is usually Denmark
• tell them to choose an animal starting with the
  second letter of the country name. (this is
  usually an elephant.
• ask then to think of what colour they associate with
  this animal (this is usually grey)
• ask them if they are thinking of a grey elephant
  from denmark...watch the surprise on their face
  when you get it right

When they have got to the country you could ask them to choose
the last letter, "k", and think of an animal. This is usually a
kangaroo or a koala, now ask them to think of a fruit begining with
the last letter of the animal then tell them it is either an apple or an orange.

Ghislain

[vigilance]

The internet always references Tesla and his quote on 3, 6, 9 (if he really said it, many attributions popular on the internet are spurious):

“If you only knew the magnificence of the three, the six and the nine… then you would have a key to the universe.”

But it's also mentioned in Aesch Mezareph (the author is talking about the columns of his squares):

'And all the columns and lines, as well from the bottom to the top, as from the right to the left, and from one angle to another, give the same sum and thou mayest vary the same ad infinitum. And the various totals always observe this principle, that their lesser number is always 3, 9, or 6 ; and again, 3, 9 or 6 and so on. Concerning which I could reveal many things to thee.'

I found this out, when dealing with the factors of 360 - whole number divisions of the circle. The digital root of the angles when dividing by 3, 6, 12, 15, 24, 30, and 60 always come out to 3, 6 or 9. The basic pattern is 3, then bisected for 6, then bisected for 12, and then 24. But also 15, 3x5, and those bisected for 30 and again for 60.



It doesn't work out for 9 or 18. 9 Does it's own thing, with 9-18-36 eventually running a pattern of 1 to 9. 45 runs the pattern 9-to-1 instead.



And factors of 4 and 5 that don't figure in elsewhere gives 9s.

[Tannur]

Interesting pattern Awani.

Notice how the sum of digits required is just 222(a+b+c) for any generic three digit number "abc". This is because when we permute the digits 6 times as shown by Awani, we end up with the a digit appearing exactly twice in each position (eg for a in the 100th position, it appears once for abc and once for acb - exactly twice in 100th position). So overall, we end up with 200a, 20a, 2a and similarly for b,c; ie overall 222(a+b+c).

Now notice also that the sum of digits of a number when applied over and over again is the same as its remainder when divided by 9. For example, for 4768 the remainder is 529*9+7 - remainder 7. And indeed, if we add digits over and over again we get 4+7+6+8=25 and 2+5=7. It isn't too difficult to prove this.

So for 222(a+b+c) we see that the sum of digits is just remainder when divided by 9. For the largest three digit number, this is 222(9+9+9), ie it is a multiple of 9, so it can only be 9. So it starts off at 9. Then notice that when we subtract 1 to get 998, the overall sum of the 6 permutations will just be 222(9+9+8). In other words, in terms of the remainder when divided by 9, we are just losing 222, or a remainder of 6 (since this is the digit sum of 222). So from 9, we go down to 9-6=3. So for 998 the answer is 3.

So really we are just working with remainders when divided by 9. 9, 3, then 3-6=-3, but as a remainder with respect to 9 this is 9-3=6. So 9,3,6. We can carry on like this to get 9,3,6,9,3,6,...

So this also applies to 4 digit numbers but the digit sum this time is the remainder of 6666(a+b+c+d) when divided by 9. It starts off with 9999 giving 6666(9+9+9+9) which leads to 9 (since divisible by 9). Then 6666(9+9+9+8) we lose 6666 which is just 24 or 2+4=6 with respect to 9. So as before, we start with 9 and lose 6 each time. So it is exactly the same pattern as before: 9,6,3,9,... You can verify this by actually carrying out the additions.

[vigilance]

Take a number.. 72 subtract the opposite 27..

72
27

45


It'll always be a factor of 9. There's a name for this I believe. don't know what it is.. i don't think its "the rule of 9"

[Tannur]

Take a number.. 72 subtract the opposite 27..

72
27

45


It'll always be a factor of 9. There's a name for this I believe. don't know what it is.. i don't think its "the rule of 9"

Nice. This is similar to Awani's one.

I don't know the rule but if we consider a random number "ab" it is really 10a+b. E.g. 72=10*7+2. Its permutation is 10b+a. Subtracting we get 9(a-b), which is a multiple of 9. But above I stated the rule that the remainder when a number is divided by 9 is the same as its ultimate digit sum when divided by 9 (eg 47567 - remainder when divided by 9 is 2 and its digit sum is 29 and 2+9=11 and 1+1=2). Hence digit sum of subtraction result will always be a multiple of 9.

[vigilance]

Nice. This is similar to Awani's one.

I don't know the rule but if we consider a random number "ab" it is really 10a+b. E.g. 72=10*7+2. Its permutation is 10b+a. Subtracting we get 9(a-b), which is a multiple of 9. But above I stated the rule that the remainder when a number is divided by 9 is the same as its ultimate digit sum when divided by 9 (eg 47567 - remainder when divided by 9 is 2 and its digit sum is 29 and 2+9=11 and 1+1=2). Hence digit sum of subtraction result will always be a multiple of 9.

Are you familiar with Ars Combinatoria? Art of Memory? Abulafia in terms of mystical permutating? etc? Lull's system?

[Tannur]

Are you familiar with Ars Combinatoria? Art of Memory? Abulafia in terms of mystical permutating? etc? Lull's system?

Yes, yes, no, no.

In my opinion, magic and things like that mean nothing without gnosis.