Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?

Three Gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one God. The Gods understand English, but will answer all questions in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

1. It could be that some God gets asked more than one question (and hence that some God is not asked any question at all).
2. What the second question is, and to which God it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
3. Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
4. Random will answer “da” or “ja” when asked any yes-no question.

What would your three questions be?

There is a small town on the East Coast that has 2 barbershops each with a single barber, and on opposite sides of town. The barbershop in the good part of town is immaculate. The floors and windows are washed and the air is fresh. The barber is very friendly, always smiling, he has shined shoes, a nice head of hair, and a clean dress shirt. The barbershop in the bad part of town is a mess. The entire barbershop is covered with a layer of dirt, and the air smells of trash. The barber always has a frown on his face. His skin is oily, his hair is ragged, and there are always stains visible on his shirt.

A man comes into town and hears of both barbershops and the man decides to go to the dirty barbershop in the bad part of town. Why does he do this?

A man lives on the tenth floor of a building. Every day he takes the elevator to go down to the ground floor to go to work. When he returns he takes the same elevator to the seventh floor and walks up the stairs to reach his apartment on the tenth floor. If there is someone else in the elevator with him or if it was raining that day, he goes back to the tenth floor directly.

Note that there is nothing wrong with the elevator or the design of the building. It’s a perfectly normal elevator in a perfectly normal building.

He hates walking up the stairs, so why does he do it?