# Number sequence



## robert@fm (Aug 22, 2018)

Given the sequence:

1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221...

1) What is the next number?

2) For bonus points, what is the simple rule that governs generating the next number?


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## robert@fm (Aug 22, 2018)

Hint: Apart from the first, each term always has an even number of digits.


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## mikeyB (Aug 22, 2018)

My figuring out may be wrong...

1321131112311311121211

The rule is that the following number describes all the elements of the previous number, as 1 then 11 because there is one 1, then 21 because 11 contains two ones, ie 21. 

I used to do mathematical problems for fun when they appeared regularly in the New Scientist.


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## robert@fm (Aug 22, 2018)

You got it right, except that you somehow accidentally got a spurious 1 in the middle of your 22.  So the last digits should be 2211, not 21211. However, I credit you wit a win, since it was probably a typo.

One question I have is, can a 4 ever enter this sequence? I don't think so.


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## mikeyB (Aug 23, 2018)

Phew. Took me 20 minutes once I’d figured out the sequence.

Ok, for revenge, here’s one of my favourites- 

A solid ball, 2 inches in diameter, has a hole drilled through the middle along a diameter. What’s the volume of material left in the ball?


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