A very vicious dog is tied to a tree. If you came close enough, you'ed lose your head. If he sees you, he'll follow your every step. Your basket ball rolls past the dog. If you are alone, how do you get your ball back with out being mutilated?
Walk around the tree until there is no more rope left on the dogs leash. Then, grab your ball.
Using only and all the numbers 3, 3, 7, 7, along with the arithmetic operations +,-,*, and /, can you come up with a calculation that gives the number 24? No decimal points allowed.
[For example, to get the number 14, we could do 3 * (7 - (7 / 3))]
Sally and her younger brother were fighting. Their mother was tired of the fighting, and decided to punish them by making them stand on the same piece of newspaper in such a way that they couldn't touch each other. How did she accomplish this?
Sally's mother slid a newspaper under a door and made Sally stand on one side of the door and her brother on the other.
You are standing in a pitch-dark room. A friend walks up and hands you a normal deck of 52 cards. He tells you that 13 of the 52 cards are face-up, the rest are face-down. These face-up cards are distributed randomly throughout the deck.
Your task is to split up the deck into two piles, using all the cards, such that each pile has the same number of face-up cards. The room is pitch-dark, so you can't see the deck as you do this.
How can you accomplish this seemingly impossible task?
Take the first 13 cards off the top of the deck and flip them over. This is the first pile. The second pile is just the remaining 39 cards as they started.
This works because if there are N face-up cards in within the first 13 cards, then there will be (13 - N) face up cards in the remaining 39 cards. When you flip those first 13 cards, N of which are face-up, there will now be N cards face-down, and therefore (13 - N) cards face-up, which, as stated, is the same number of face-up cards in the second pile.
A fancy restaurant in New York was offering a promotional deal. A married couple could eat at the restaurant for half-price on their anniversary. To prevent scams, the couple would need proof of their wedding date. One Thursday evening, a couple claimed it was their anniversary, but didn't bring any proof. The restaurant manager was called to speak with the couple. When the manager asked to hear about the wedding day, the wife replied with the following: "Oh, it was a wonderful Sunday afternoon, birds were chirping, and flowers were in full bloom." After nearly 10 minutes of ranting, she comes to tell him that today was their 28th wedding anniversary.
"How lovely", the manager said, "However, you do not qualify for the discount. Today is not your anniversary, you are a liar".
How did the manager know that it wasn't their anniversary?
The calendar repeats itself every 28 years. So, if they were married on a Sunday 28 years ago, the day they were at the restaurant would also have to be a Sunday. Since it was a Thursday, the manager knew they were lying, and abruptly kicked them out of his restaurant.
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
You have two lengths of rope. Each rope has the property that if you light it on fire at one end, it will take exactly 60 minutes to burn to the other end. Note that the ropes will not burn at a consistent speed the entire time (for example, it's possible that the first 90% of a rope will burn in 1 minute, and the last 10% will take the additional 59 minutes to burn).
Given these two ropes and a matchbook, can you find a way to measure out exactly 45 minutes?
The key observation here is that if you light a rope from both ends at the same time, it will burn in 1/2 the time it would have burned in if you had lit it on just one end.
Using this insight, you would light both ends of one rope, and one end of the other rope, all at the same time. The rope you lit at both ends will finish burning in 30 minutes. Once this happens, light the second end of the second rope. It will burn for another 15 minutes (since it would have burned for 30 more minutes without lighting the second end), completing the 45 minutes.
