Its nice when games have riddles hidden in them. While playing TES:Arena, I came across an unusual logical puzzle:
There are 3 cells.
If Cell 3 holds worthless brass, Cell 2 holds the gold key.
If Cell 1 holds the gold key, Cell 3 holds worthless brass.
If Cell 2 holds worthless brass, Cell 1 holds the gold key.
Knowing this brave fool, and knowing that all that is said cannot be true, which cell contains the gold key?
The correct answer is Cell 2 as suggested by the game. I wanted to know how one could logically arrive at the result. Could anyone help me with this?
What I tried: I negated all the above statements. The first implication became Cell 3 holds worthless brass AND Cell 2 does not have gold key. But if this is true, then cell 2 does not have the gold key and the result is incorrect. Hence I had this doubt.
PS: Choosing the wrong door causes man eating spiders to be released.
Best Answer
If you label the conditions a-c, and if the gold key exists and is unique, it is enough to show that not in 2 leads to a contradiction. But 'key not in 2' leads to 'key in 2' (so a contradiction), as follows:
By (c), not in 2 implies in 1. By (b) then, not in 3. By (a) then, key is in 2. Contradiction.
To be safe, you can check if the game makers messed up:
As 'key in 1' is a sub chain of the above, it also leads to 'key in 2'. Contradiction.
Similarly, 'key in 3' means by uniqueness that 2 holds brass, which, by (c), implies 1 holds the key. Contradiction.
Finally note that if the key is in 2, it doesn't lead to any contradictions. So game is correct.