I recently tried to come up with "random" mental calculation exercises in an attempt to fight traffic jam boredom. Unfortunately, I quickly got bored by the lack of creativity of the problems I can generate for myself.
My question is: Are there any standard patterns that can generate a sequence of mental calculation problems? Ideally the generation scheme
- should not require any tools like smartphones
- should not depend excessively on random number input (because e.g. in a traffic jam you are surrounded by the same number plates and it would be nice not to depend on being surrounded by numbers, which typically have a bias)
- should generate problems that cover a broad range of arithmetic challenges.
The first thing that came to my mind is a pattern like the Collatz conjecture. The problem is that the arithmetic operations are very limited and it still requires a random number starting seed, but at least the sequence can keep me busy for a while. On the other hand, other sequences that came to my mind (e.g. terms of a Taylor series) were a bit too much for a traffic jam. Is there anything in-between?