How much information = How many yes/no questions

Simon and dad were having a discussion about how difficult it is to solve a 3×3 blindfolded and whether that requires a different set of skills than simply solving a 3×3 (short-term as opposed to long-term memory, possibly), and whether a multiblind solve requires an even more different set of skills. Simon has managed to do a blind solve successfully once and knows the way to go about it, but in this more general discussion, he was interested in the mathematical odds of memorizing the scramble correctly. He asked himself this question:

How many times do you have to ask a yes/no question in order to describe a random 3×3 scramble?

Considering a 3×3 cube has over 43 quintillion possible permutations, Simon reasoned…

to answer the question, how many yes/no question you have to ask yourself to describe a random scramble, you can calculate the log₂ of that number. He quickly typed this in Google search bar, which is the same as log₂(4,325200327449e19):  

The result he got was just over 65. That’s how much information you would have to hold in your short-term memory if you want to solve a 3×3 blindfolded, Simon explained, in bits. “Because a bit is one yes/no question to ask before you know the answer, literally. It’s like you have these 43 quintillion permutations and you have to get back to one — how many steps do you need to take? 65 bits, that’s a lot to put in your short-term memory, your short-term memory is going to struggle!”

Simon told me that humans generally tend to have much better long-term than short-term memory.

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