The Market Scales Puzzle

 

It would be interesting to look more into the concepts behind why these problems work out the way they do. For example, the nice properties we get when working with base 2 and the reasons we have binary representations of numbers. We could also consider how one might generalize the problem by developing a general formula for n weights. This problem was another great example of the "low floor, high ceiling" math problems which can engage a wide range of learners. Definitely reminds me of material covered in my Number Theory course with regards to working in binary as well as in other bases. I also originally thought there might be a connection to modular arithmetic and equivalence classes but I don't believe that was the case. 

Thanks for reading,

Josh