Author: Zoey

This is the solution to Challenge #3 – The Devil’s Tail, make sure you check that post out before looking at the solution!

This Challenge is a modification of a famous problem which confused many people – The Boy-Girl paradox.

So, it turns out that “Heads” is the most probable at 67%. But why?

The devil could have any of the 3 combinations: {HT, TH, TT}, and 2 of those include a Heads! A common answer is “Equally Likely” as it is easy to assume that the devil showed us a specific coin, meaning the remaining coin is equally likely to be Heads or Tails, but this is not the case as we do not know which coin the devil showed us. Some people’s intuition may also have lead them to think it might be Tails as we have already had a Tails, but this is also not true. Hopefully this problem illustrates how probability is very deceptive and counter-intuitive!

This is the solution to Challenge #2 – The Elements, make sure you check out the challenge before looking at the solution!

Trust the devil. Why?

The first clue given in the challenge is the note left behind by Doctor Aro.

The key piece of information on the note says that we have to reflect on the odd things in life.

Reflecting the position of the digits in the odd numbers we get:
71 6 53 9 68
(Reflecting the position of the digits for 9 leaves it the same)

But how do we decipher the numbers?

Dr Aro was ‘dabbling in the chemical arts’ and this challenge is called ‘The Elements’, written in a similar way to the elements in the periodic table.

Using the periodic table we get:
Lu-C-I-F-Er

Lucifer i.e. the devil 😈

Were you able to save Doctor Aro?

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.