When I was young I used to spend the time of the sermon at the mass, which I considered quite boring, by using my fingers on my legs to represent the digits in base 2 and counting from 0 to 1023. However, not only half of the movements would require more than one finger to move simultaneously but my right hand little finger would do a lot of work, moving 1023 times, while the other fingers would do gradually less work, up to my left hand little finger which would move only once. This was quite a good piano exercise for the 4th and 5th fingers of the right hand (I was studying piano by then), but it wasn't well balanced for all the fingers.
I started thinking at first if it were a possibility to go through all combinations by moving only one finger at a time, without repeating combinations in the process. I recently found out that not only that is possible, but it also is quite a simple thing to do.
However, my main problem still remains up to this day: how can I balance a sequence of all combinations from 0000000000 to 1111111111 so that all the finger work-out is well distributed by all fingers? Since there are 1023 movements in total, I realise it is impossible to have the fingers do exactly the same amount of movements, but can we find a sequence where seven of them move 102 times and the other three move 103 times? If not, how close can we get to these values? How balanced can a sequence be?
I think you are looking for a “balanced Gray code.“ https://en.wikipedia.org/wiki/Gray_code#Balanced_Gray_code