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Laura007

magic trick

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I have no idea but it so happens that the sum of the 2 digits of a 2 digit number when subtracted from the original number will be divisible by 9. Probably to do with using base 10?

 

Hang on - I left school 20 years ago and uni 13 years ago so I dont care. I am happy to do my sons homework with him which involves sticking pictures beginning with the letter p in a book!!

 

Good trick anyway which will baffle you if its only done once.

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Shona, you and Gina both have a good excuse for not understanding it. All those pregnancy hormones - I'm convinced that these babies take over the brain as well as the belly :wink:

Me, on the other hand :roll: Let's say that no-one's ever going to describe me as a mathematical genius :shock:

I'm off to read that explanation again, maybe I'll finally get it if I concentrate hard enough :?

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Every time you click and open up the page it has a different set of symbols for each number. The mathmatical act of subtracting the sum of two digits from the original two digit number produces a number which is divisible by 9 (don't ask me how!)

 

So - every number which is divisible by 9 is given the same symbol and therefore it always 'knows' the answer to show.

 

I think......... :?

 

Check it by staying on the same page and writing down a few...

21 = 18

39 = 27

47 = 36

56 = 45

64 = 54

 

Check on all these answers on the same page - they will all have the same symbol

Start again and look - all the numbers divisible by 9 will have the same symbol - but a different one to the previous page

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Ah. So you mean only numbers that are multiples of 9 work, and they all have the same symbol. So each time only 1 symbol will work.

 

I think you're right - if I choose another symbol at random, it fails! So I'm not so transparent after all!

 

Good trick all the same!

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Here is a simple proof that subtracting the sum of the digits of a two digit number from that number is always divisible by 9.

 

Now, I don't want any panicking because it's algebra. And pay attention at the back there!

 

Two digit number is always 10x+y (x is the tens, y is the units)

 

Sum of the digits is x+y.

 

(10x+y)-(x+y) = (9x+x+y)-(x+y) = 9x

 

In other words, the answer is always 9 times the tens of the original number.

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