You and a friend are standing in front of two houses. In each house lives a family with two children.
"The family on the left has a boy who loves history, but their other child prefers math," your friend tells you.
"The family on the right has a 7-year old boy, and they just had a new baby," he explains.
"Does either family have a girl?" you ask.
"I'm not sure," your friend says. "But pick the family that you think is more likely to have a girl. If they do have a girl, I'll give you $100."
Which family should you pick, or does it not matter?
You should pick the house on the left. Specifically, there is a 2/3 chance that the family on the left has a girl, whereas there's only a 1/2 chance that the house on the right has a girl.
This is a very counterintuitive riddle. It seems like there should always be a 1/2 chance that a given child is a girl. And in fact there is. The key word there is "given". Because we are not asking about a "given" child for the house on the left. We are asking about what could be either child. Whereas for the house on the right, we are asking about a "given" child...specifically, we're asking about the younger child.
There are 3 possibilities for the children in the first house:
Younger Older
Girl Boy
Boy Girl
Boy Boy
There is no "Girl, Girl" option because we know the house on the left has at least one boy. Since each of these 3 options is equally likely, and 2 of them have one girl, there is a 2/3 chance of there being a girl in the house on the left.
For the house on the right, because we already know the older child is a boy, there are only two possibilities:
Younger Older
Girl Boy
Boy Boy
And as we can see, there is a 1/2 chance for the house on the right having a girl.
Search for: Boy or Girl paradox
A farmer needs to cross a river with a fox, a chicken, and a bag of cornmeal. He has a small boat that can only carry himself and one item at a time.
If left alone together on either bank without the farmer present:
The fox will eat the chicken.
The chicken will eat the cornmeal.
How can he get everything safely to the other side?
Take the chicken across to the far bank (leaves fox and cornmeal together on the near bank—safe).
Return empty-handed to the near bank.
Take the fox across to the far bank.
Bring the chicken back to the near bank (leaves the fox alone on the far bank—safe).
Take the cornmeal across to the far bank (leaves fox and cornmeal together on the far bank—safe).
Return empty-handed to the near bank (leaves the chicken alone on the near bank).
Take the chicken across to the far bank.
I'm a fruit. If you take away my first letter, I'm a crime. If you take away my first two letters, I'm an animal. If you take away my first and last letters, I'm a form of music. What am I?
While mixing sand, gravel, and cement for the foundation of a house, a worker noticed a small bird hopping along the top of the foundation wall. The bird misjudged a hop and fell down one of the holes between the blocks. The bird was down too far for anyone to reach it and the hole was too small for it to fly out of. Someone suggested using two sticks to reach down into the hole and pull the bird out, but this idea was rejected for fear it would injure the fragile bird. What would be the easiest way to get the bird out of the hole without injuring it?
Since they had plenty of sand available, they could pour a little at a time into the hole. The bird would constantly keep shifting its position so that it stood on the rising sand.
A black dog stands in the middle of an intersection in a town painted black. None of the street lights are working due to a power failure caused by a storm. A car with two broken headlights drives towards the dog but turns in time to avoid hitting him. How could the driver have seen the dog in time?
Pete is a worker on a large ship with hundreds of other men. He is constantly making mistakes, tying ropes the wrong way, steering the ship the wrong way, and making other blunders. One time he accidentally caused the ship to get stuck in a shallow shore, causing thousands of dollars in damage.
However, when Steve, the captain of the ship, is asked about Pete, Steve says "I wish we had five men like Pete on this ship."
Why would he say this?
Unfortunately for the ship, there are dozens of men who are as inept as Pete is.
Captain Steve wishes there were FEWER men like Pete on the ship, since there are currently far more than five.
It was a man's birthday. He lay dead in the lounge room of his house. Next to his body was a note, written in pencil. The note read 'Happy Birthday, Friend'. The victim had a girlfriend and the police suspected her ex-boyfriend. They could find no obvious evidence. While searching the ex-boyfriend's car, the police saw an envelope with the girlfriend's address written on it. They thought they would get the handwriting checked against the note. The scientist in charge came in early to work the next day; it was 7am. He looked out his window which faced east and stared at the rising sun and it was then that he realised how to prove the ex-boyfriend killed the man, even though the girlfriend's address was not written in the same handwriting. How did he do it?
The scientist's office faced east, and the sun was coming in through the window at a very low angle. He saw some very faint shadows on the surface of the envelope. He looked closer. There were the words embossed on the paper. They read "Happy Birthday, Friend". The ex-boyfriend had forgotten that a pencil leaves an impression on paper beneath the page written on.
