Yeah, I noticed that too. Treating a byte as eight tally marks misses the point about the combinatorialnature of place settings.

It's not 100% wrong, because bit shifting and bit packing are real-world applications used in memory all the time.

But these are not the only possible values:

  00000001
  00000010
  00000100
  00001000
  00010000
  00100000
  01000000
  10000000

It's not incorrect to make a decision to limit one's input to those values, but it is incorrect to presume that binary data can only be recorded that way.

Treating those 8 place settings as eight lightbulb circuits that each need an individual test isn't the right mindset for someone performing compiler optimization.