כל התרגומים

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

What is the expected number of bits in the bars that are between two adjacent bad bars?

Could it be that some of the 20 solutions for this kind of chocolate gift is related to prime numbers?

Let's say that the gold chocolate spheres of the inner part of the gift count p, q & r spheres in each dimension.

Question: Is there a chocolate gift, satisfying the Yoshigahara's conditions, using prime numbers in some or all p, q & r?