IBM Ponder This #156 · April 2011

A wiggly plastic snake is composed of 20 segments. Assuming you start with a left turn, how many ways can the snake's other 18 joints be bent in 90-degree angles, either to the left or to the right, in such a way that the snake does not overlap/touch itself?

Thanks to Vi Hart for raising the question in her beautiful blog (link resides outside of ibm.com).

Bonus question: If you subtract the number of English letters from the answer, what is the connection of the result to the year 2010?

Solution

Best opened after a real attempt

To be added.