This is the solution to Challenge #1 – Prison Break – make sure you check that post out if you haven’t already!
It turns out that Guard C is your friend!
We are given the information that each robot guard always lies for the whole day, or always tells the truth for the whole day. This information does not indicate that the guards have truth/lie days in any particular order.The robot guards could have truth/lie days as follows: Truth, Lie, Truth, Lie, …
But equally could have days as below:
Truth, Truth, Truth, Lie, …
There is no reason to presume that the guards all follow the same orders, so we can assume that each guard is independent of the others. This means a guard’s truth/lie days can be different to the other guards.
So why is Guard C our friend? Guard C said “Today, I lie.”
- If Guard C is telling the truth, then it means Guard C is lying as indicated from the statement.
- – If Guard C is lying, then Guard C has just told us the truth about lying.
Guard C’s statement is a paradox!
Paradoxes like the one presented in this challenge, also known as “Liar’s paradox”, are attributed to the ancient Greek seer Epimenides (fl. c. 6th century BCE). Epimenides, an inhabitant of Crete, famously declared that “All Cretans are liars”.
This paradox will arise whenever the statement refers to whoever is claiming the lie themself.
Consider: “This sentence is a lie”.
This circular logic is important in part because it creates severe difficulties for logically rigorous theories of truth; it was not adequately addressed (which is not to say solved) until the 20th century.