On: A liar who always lies says "All my hats are green...

[MrMcCall]

Thanks for breaking that down for me.

I guess, to me, a programmer logician not a mathematician logician, the real problem for me here is the definition of "liar" as it applies to how we parse the problem statement's facts.

[n4r9 → MrMcCall]

I'd argue that this bit of mathematical logic carries over to many programming languages. For example using LINQ expressions in C#:

https://dotnetfiddle.net/3QGurc