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there are actually 10 problems: naming things, cache invalidation, base conversions, off by one errors, and cache invalidation

Base conversions are easy, but which off by one is it? base 4 or base 6?

10 base 2 is 2 base 10. i gave four unique hard problems. and now typing this out i see that I was off by 1 (or two)

Off-by-two is a subset of all possible off-by-one errors.

All off-by-one errors can be reproduced by producing an off-by-one error of some other off-by-one error.