One answer to the Morris puzzle (there may be others)

1 11 21 1211 111221 ... What's the next number?

the numeral 1 is just one one

one one can be written as 1 1

1 1 is actually two ones.

two ones can be written as 2 1

2 1 is one two and one one

one one and one two is 1 2 1 1

1 2 1 1 is one one, one two, and two ones.

one one, one two, and two ones is 1 1 1 2 2 1.

1 1 1 2 2 1 is three ones, two twos, and one one.

So the next number is 3 1 2 2 1 1.

It took me six months to solve (and a bit of help from some friends) ... shows you what kind of cryptologist I'd make!