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Did you hear the one about...

100 by 3 by 3 by 3 by 3

SMILE!

What happens when you divide 100 by 3 by 3 by 3 by 3? (...from the question posed on the previous page)

100 / 3 / 3 / 3 / 3 = 1.23456790123456790123456790123456790...

So here's the puzzle: Why is there no '8' in the answer?

To see the answer, we must look closely at what is happening.

You'll notice that each digit in the answer is one bigger than the digit before (1.234 ~). When we reach 9, the next number should be (and is) 10. Now the '1' of that 10 is carried into the place before, making the 9 a 10. Then the '1' of that 10 gets carried into the place before, making the 8 a 9.

Let's look at the long-hand version:

   1.234567901234567890...
= 1
+ 0.2
+ 0.03
+ 0.004
+ 0.0005
+ 0.00006
+ 0.000007
+ 0.0000008
+ 0.00000009
+ 0.000000010
+ 0.0000000011
+ 0.00000000012
+ 0.000000000013
+ 0.0000000000014 etc.

And if you total that up, you get:
= 1.234567901234

(If you can think of a practical application for this nonsense, please let us know!)

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