- #1

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Example: 22 (2+2=4) 22-4=18 (1+8=9)

or

14567 (1+4+5+6+7=23 and 2+3=5) 14567-5=14562 (1+4+5+6+2=18 and 1+8=9)

Why does you always end up with 9 and is there a name for this?

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- Thread starter Dave9600
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- #1

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Example: 22 (2+2=4) 22-4=18 (1+8=9)

or

14567 (1+4+5+6+7=23 and 2+3=5) 14567-5=14562 (1+4+5+6+2=18 and 1+8=9)

Why does you always end up with 9 and is there a name for this?

- #2

CRGreathouse

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- #3

tiny-tim

Science Advisor

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Because when you replace eg 50000 by 5, you reduce the number by 5 times 9999, which is obviously divisible by 9.

Add all the 50000s etc, and add all the 5s etc, and then subtract, and the result is divisible by 9.

In numbers: ∑ a

= 9(∑ a

- #4

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

- #5

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And for a bit of fun, see

http://mensanator.com/rotanasnem/cherries/cherries.htm" [Broken]

http://mensanator.com/rotanasnem/cherries/cherries.htm" [Broken]

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- #6

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Chuckles

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