Logical Problem
Basic

Lecture Notes

Many seemingly mission-impossible brain teasers can be solved using basic logic operations. More specifically, the solutions to these problems rely on the following intuitive facts:

- TRUE and FALSE = FALSE
- not (FALSE) = TRUE
- ...

A classical example is shown below. We have two people: one is a truth-teller, which can be represented by TRUE, and the other is a liar, represented by FALSE. If we knew who was who, solving this problem would be much easier. However, since we do not know which one is TRUE and which one is FALSE, therein lies the challenge.

Despite not knowing their identities, we understand that combining TRUE and FALSE must yield FALSE. This principle is key to solving this brain teaser.

Examples

(4631) $\textbf{Two Doormen}$ Two doormen are guarding two rooms. One room contains tons of gold and the other is empty. Among these two doormen, one is honest who always tells the truth and the other is a liar who always gives false answers. While they know each other well, you do not know who is honest and who is not. If you are given just one chance to ask one question to one of them, what can you do in order to find out which room contains the gold? |