CMU Math Professor Po-Shen Loh teaches how to use "6 Bits" of your memory 

YES ABSOLUTELY

Yup. The reason is because parity (whether something is even or odd) is a binary question - meaning it only has 2 outcomes - either yes or no. The best you can do with 2 outcomes is split the search space into 2 equal halves. If you have 64 possible states in the search space (1 of the 64 squares is changed), and each operation can only half that search space, you will reach 1 after 6 halving operations. This is log base 2 of 64. Now suppose you try to solve a puzzle where the query is not binary like the one posed here ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-tE2dZLDJSjA.html. The scale has 3 possible outcomes, tilted right, tilted left or balanced. Since we have 3 outcomes, we can split the search space into 3 equal thirds at each operation. As the search space is 24 (Of the 12 coins, only 1 of them is either heavier or lighter), we need to do this 3 times to reach 1. This is the ceiling of log base 3 of 24. Given that the best solution is log base (number of outcomes of query) of (number of possibilities), the TED-Ed video could have actually posed the question with 13 coins and also allowed for the possibility that none of the coins were counterfeit. This would result in 27 possibilities, which can also be solved in 3 operations (log base 3 of 27 is 3). P.S. I remember there was also a video from either 2016 or 2017 about using prisoners to find if 1 of 1000 wine barrels had been poisoned which also uses a similar idea. The setup being that you had 10 prisoners to test 1000 barrels. Ceiling of log base 2 of 1000 is exactly 10 so you would be able to do it by making the prisoners test the wine according to its binary representation. I can't seem to find the video though. If anyone finds it can reply this comment ty.

@@jmong2871 I guess this is it: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-N3qmN6pYhi0.html