Ranting corner
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22-09-2014, 07:52 PM
RE: Ranting corner
(22-09-2014 07:50 PM)Ferdinand Wrote:  Hug

dumbass.

Haha, I know. Yes

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Ferdinand: We don't really say 'theist' in Alabama. Here, you're either a Christian, or you're from Afghanistan and we fucking hate you.
Worst
Ferdinand: Everyone from British is so, like, fucking retarded.
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22-09-2014, 07:54 PM
RE: Ranting corner
(22-09-2014 07:52 PM)Hughsie Wrote:  
(22-09-2014 07:50 PM)Ferdinand Wrote:  Hug

dumbass.

Haha, I know. Yes

So your sister ate the last snack cake again?

(31-07-2014 04:37 PM)Luminon Wrote:  America is full of guns, but they're useless, because nobody has the courage to shoot an IRS agent in self-defense
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22-09-2014, 07:56 PM
RE: Ranting corner
(22-09-2014 07:54 PM)Revenant77x Wrote:  
(22-09-2014 07:52 PM)Hughsie Wrote:  Haha, I know. Yes

So your sister ate the last snack cake again?

HAHAHAHAHA SHIT. GOODBYE REV. Weeping
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22-09-2014, 07:56 PM
RE: Ranting corner
(22-09-2014 07:54 PM)Revenant77x Wrote:  
(22-09-2014 07:52 PM)Hughsie Wrote:  Haha, I know. Yes

So your sister ate the last snack cake again?

Um you mean twinkie

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23-09-2014, 07:31 PM
RE: Ranting corner
So I think I'm a mathematical genius or something and just don't know it.
I was laying awake this morning thinking about the 9 times table, as you do, and I was thinking about how I always did my 9 times tables.
I would take the number before the number you were multiplying 9 by and join it up with the amount required to get to 10.

ie: 9*6 = 54
5 is the number before 6
4 is the amount required to get 6 to 10.

ie2: 9*7 = 63

It was always a quick way I did the 9 times tables and I found easier then the bullshit method they taught us in school.
So I had never really used it beyond 10 because it doesn't work.

ie: 9*12 = 118
Which is wrong because as we all know 9*12 is 108.

BUT I noticed a pattern. For numbers between 11-20 if you took two numbers prior you would get the right answer.

ie2: 9*12 = 108
10 is 2 numbers before 12
8 is required to get to 20

But then I noticed another pattern.

ie: 9*45 = 405
40 is 5 less then 45
5 is required to get to 50.

So the pattern becomes, you take the number before equal to the tenth rounded up and then join it with the number required to get to the next tenth.

ie: 9*4537
4537 is in the 454th 10th bracket. 4531 to 4540
If it was 6987 is would be the 699th tenth bracket.

So, you take the bracket that it belongs too, in this case 454, and you subtract it from the number. 4537-454 = 4083
3 is required to round the number up to the nearest 10th.
Thus: 9*4537 = 40833

Check it on a calculator if you don't believe me, I guarantee it's correct.


And thus, multiply any number by 9 in your head.
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24-09-2014, 05:29 AM
RE: Ranting corner
(23-09-2014 07:31 PM)earmuffs Wrote:  So, you take the bracket that it belongs too, in this case 454, and you subtract it from the number. 4537-454 = 4083
3 is required to round the number up to the nearest 10th.
Thus: 9*4537 = 40833

Where did that magical 3 come from?

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24-09-2014, 06:18 AM
RE: Ranting corner
So what you're saying is that in base n,
x*(n-1) = x*n - x = (x-1+1)*n - x = (x-1)n + (n-x) = one less than x in the ns column and the difference between n and x in the 1s column
eg x*9 = one less than x in the 10s column and the difference between 10 and x in the 1s column, eg 4*9 = 36 (3 = one less than 4, and 6 = 10-4).
That's fine, and proven above.

I'm having trouble with your general case. You say you can calculate a bracket as the nearest 10th, where 5 is and below are rounded down while 6 and up are rounded up. The final digit is 10-the-original-final-digit. However, calculating this I found the bracket was off periodically if I rounded only to the nearest 10. I had to round to the nearest 9 to cancel out the errors:

Input Bracket=INT((A4+5)/10) Brackt Rem=MOD(-A4,10) Estimate=(A4-B4)*10+C4 Caculated Difference
4530 453 0 40770 40770 0
4531 453 9 40789 40779 -10
4532 453 8 40798 40788 -10
4533 453 7 40807 40797 -10
4534 453 6 40816 40806 -10
4535 454 5 40815 40815 0
4536 454 4 40824 40824 0
4537 454 3 40833 40833 0
4538 454 2 40842 40842 0
4539 454 1 40851 40851 0
4540 454 0 40860 40860 0
4541 454 9 40879 40869 -10
4542 454 8 40888 40878 -10
4543 454 7 40897 40887 -10
4544 454 6 40906 40896 -10
4545 455 5 40905 40905 0

I think your estimate is only correct 60% of the time. 40% of the time it is to low by 10.

Give me your argument in the form of a published paper, and then we can start to talk.
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24-09-2014, 06:23 AM
RE: Ranting corner
(23-09-2014 07:31 PM)earmuffs Wrote:  So I think I'm a mathematical genius or something and just don't know it.
I was laying awake this morning thinking about the 9 times table, as you do, and I was thinking about how I always did my 9 times tables.
I would take the number before the number you were multiplying 9 by and join it up with the amount required to get to 10.

ie: 9*6 = 54
5 is the number before 6
4 is the amount required to get 6 to 10.

ie2: 9*7 = 63

It was always a quick way I did the 9 times tables and I found easier then the bullshit method they taught us in school.
So I had never really used it beyond 10 because it doesn't work.

ie: 9*12 = 118
Which is wrong because as we all know 9*12 is 108.

BUT I noticed a pattern. For numbers between 11-20 if you took two numbers prior you would get the right answer.

ie2: 9*12 = 108
10 is 2 numbers before 12
8 is required to get to 20

But then I noticed another pattern.

ie: 9*45 = 405
40 is 5 less then 45
5 is required to get to 50.

So the pattern becomes, you take the number before equal to the tenth rounded up and then join it with the number required to get to the next tenth.

ie: 9*4537
4537 is in the 454th 10th bracket. 4531 to 4540
If it was 6987 is would be the 699th tenth bracket.

So, you take the bracket that it belongs too, in this case 454, and you subtract it from the number. 4537-454 = 4083
3 is required to round the number up to the nearest 10th.
Thus: 9*4537 = 40833

Check it on a calculator if you don't believe me, I guarantee it's correct.


And thus, multiply any number by 9 in your head.



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24-09-2014, 06:58 AM
RE: Ranting corner
x*(n-1) = x*n - x = (x-1+1)*n - x = (x-1)n + (n-x)
So this is straightforward in cases where x <= n. However, what if x > n? Can we do anything with modulo arithmetic?

The last digit of the product is x*(n-1) % n.
x*(n-1) % n = xn - x % n = -x%n = n - x%n
eg the last digit of x*9 = x*9 % 10 = 10 - x%n
eg the last digit of 4532*9 = 10 - 2 = 8
This is a generalisation of the first case, where the last digit of the product can always be calculated as 10 - the last digit of the input.

The problem comes in estimating the bracket the product should fall into to get the other digits. I found I had to add 9 before rounding down to make this work consistently. ie INT((x+9)/10), and we still need to perform a subtraction to after this.

Instead maybe we should focus the form x(n-1) = xn - x so that only one subtraction is required, eg 9*x = 10*x - x, eg 9*4532 = 45320 - 4532 = 40788?
Or use a calculator, of course Smile

Give me your argument in the form of a published paper, and then we can start to talk.
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24-09-2014, 07:26 AM
RE: Ranting corner
(24-09-2014 05:29 AM)Chas Wrote:  
(23-09-2014 07:31 PM)earmuffs Wrote:  So, you take the bracket that it belongs too, in this case 454, and you subtract it from the number. 4537-454 = 4083
3 is required to round the number up to the nearest 10th.
Thus: 9*4537 = 40833

Where did that magical 3 come from?

3 is required to get to 10.
In this case to get 4537 to 4540.

Quote:You say you can calculate a bracket as the nearest 10th, where 5 is and below are rounded down while 6 and up are rounded up.

No sorry, that's my bad wording.
You round up, always up. 1-10, 11-20, 21-30, 378-380, 68243-68250.

The equation would be: (brace yourself for my attempt at making this into an equation)

Where 'n' is the last digit of 'N' and 'N' is the number you're multiplying by 9.

N - ((N + (10 - n)) / 10) = C *insert push together symbol here* (10 - n)

ie: 763

763 - ((763 + (10 - 3)) / 10) =
763 - ((763 + 7) / 10) =
763 - 77 = 686
686 *insert push together symbol here* (10 - 3)
So the answer is: 6867
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