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Fascinating numbers...

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Fascinating numbers...

Spurred on from the arithmetical thread I thought I'd start one on how fascinating numbers can be...
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Choose a four digit number (the only condition is that it has at least two different digits).
Arrange the digits of the four digit number in descending then ascending order.
Subtract the smaller number from the bigger one.
Repeat.
Eventually you’ll end up at 6174, which is known as Kaprekar’s constant. If you then repeat the process you’ll just keep getting 6174 over and over again.

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Take 1 + √3 and 1 − √3 and add them together - what do you get? It works for all values of x (1 + √x and 1 − √x)

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111,111,111 × 111,111,111 = 12,345,678,987,654,321

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18 is the only positive number that is twice the sum of its digit

Any more...?

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Re: Fascinating numbers...

153 is the first in a sequence being the cube of its components, next (excluding zeros) is 371. 
153 is also the sheet number of the Michelin map of the Western Sahara, there is an strange club called the 153 club ,of which there were 153 members, to be eligible for membership you must have traveled across Michelin map 153.
153 is the sum of the first 17 integers and the sum of factorial 1-5 ie 1!+2!+3!....5!............
Broken down to variations of 1 and 5 and 3
153 + 513 = 666       
315 + 351 = 666       
135 + 531 = 666
and so on
alanf
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Re: Fascinating numbers...

If this is the sort of thing that interests you then I suggest having a look at Numberphile.
http://www.numberphile.com/
VileReynard
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Re: Fascinating numbers...

The sum of the numbers on a roulette wheel = 666...
The sum of all entries in an n×n multiplication table equals [n(n+1)/2]^2.

St3
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Re: Fascinating numbers...

feels like back at school . borrrrrringggggggggggggggg  Cheesy
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Re: Fascinating numbers...

42
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Re: Fascinating numbers...

21 (9+10) - ask a teenager  Wink
Call me 'w23'
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Re: Fascinating numbers...

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gswindale
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Re: Fascinating numbers...

Quote from: Mav
Spurred on from the arithmetical thread I thought I'd start one on how fascinating numbers can be...

Quote
Take 1 + √3 and 1 − √3 and add them together - what do you get? It works for all values of x (1 + √x and 1 − √x)


That isn't particularly surprising seeing as you are simply doing the following
1 + 1 + √x - √x or even simpler
1 + 1
Razorback
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Re: Fascinating numbers...

The one that has always interested me is that if you keep adding consecutive odd numbers together the result is always a square number.
1+3 = 4 + 5 = 9 + 7 =16 + 9 =25 etc.
VileReynard
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Re: Fascinating numbers...

That's ultimately because
(n + 1)^2 = n^2 + (2n + 1)

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Re: Fascinating numbers...

To find out if any number irrespective of number of digits  is divisible by 3, simply add all the digits together. If the sum is divisible by 3, then the original number is divisible by 3. You can continually add the risks together until you reach a single digit, the formula still works.
VileReynard
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Re: Fascinating numbers...

I found this on http://planetmath.org ; Grin Grin
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With this simple short cuts you can find out a number is divisible by a given number Divisible by 2: A number is divisible by 2, if its unit’s digit is any of 0, 2, 4, 6, 8. Example: 6798512
Divisible by 3: A number is divisible by 3, if sum of its digits divisible by 3. Example : 123456 1+2+3+4+5+6 = 21 21 is divisible by 3 so 123456 is also divisible by 3
Divisible by 4: if the last two digits of a given are divisible 4, so the number can be divisible by 4. Example : 749232 Last two digits are 32 which are divisible by 4 so the given number is also divisible by 4
Divisible by 5: If unit’s digit of a number is either ‘0’ or ‘5’ it is divisible 5. Example : 749230
Divisible by 6: If a given number is divisible by 2 and 3 (which are factors of 6), then the number is divisible by 6. Example : 35256 Unit’s digit is 6 so divisible by 2 3+5+2+5+6 = 21 so divisible by 3 So 35256 divisible by 6
Divisible by 8: if last 3 digits of a given number is divisible 8, then the given number is divisible 8. Example: 953360 360 is divisible by 8, so 953360 is divisible by 8
Divisible by 9: A number is divisible by 9, if sum of its digits divisible by 9. Example : 50832 5+0+8+3+2 = 18 divisible by 9 so 50832 divisible by 9
Divisible by 10: A number is divisible 10, if it ends with 0. Example : 508320
Divisible by 11: A number is divisible by 11,if the difference of sum of its digits at odd places and sum of its digits at even places , is either 0 or a number divisible by 11. Example : 4832718 (sum of digits at odd places ) – (sum of digits at even places) =(8+7+3+4)-(1+2+Cool = 11 which is divisible by 11. So 4832718 is divisible by 11.
I hope this simple tricks, will be very helpful to solve math’s homework problems easily.