One of twelve tennis balls is a bit lighter or heavier (you do not know which) than the others. How would you identify this odd ball if you could use an old two-pan balance scale only 3 times?
You can only balance one set of balls against another, so no reference weights and no weight measurements.

Answer: I would first take all 12, divide by half, put on scale
See which side lighter, then those 6
Divide again to 3-3
Once you get the lighter side
You're left with 3 balls
There are two outcomes but the method is the same
Choose two of the three, measure them
If one is lighter than another, that's your lighter ball
If they're the same, the leftover ball is the lighter ball.

You are one of 20 prisoners on death row with the execution date set for tomorrow.

Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:
“I’m gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....)

(The prisoner in the back will be able to see the 19 prisoners in front of him. The one in front of him will be able to see 18…)

Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question: WHAT IS THE COLOR OF YOUR HAT?
He will only be allowed to answer “BLACK” or “RED”. If he says anything else you will ALL be executed immediately.

If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on…

Well, good luck tomorrow, HA HA HA HA HA HA!”

Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow? How many?



 
 
 
 
 
 
 

Answer: First guy is a coin toss - let's wish him good luck.

His job is to establish the parity of black hats visible to him.

He says "Black" if he sees an odd number of black hats; "Red" otherwise.

By paying attention to what has been said, each prisoner will know his hat's color.

Example:

Second to speak hears "Black" and sees an even number of black hats.

He knows his hat is black [odd changed to even - must be his is black] and says "black".

Third guy has heard "black" and "black" and sees an even number of black hats.

He knows his hat is red [even stayed even - his hat can't be black] and says "red".

And so on, to the front of the line.

General algorithm:

The first time you hear "black", say to yourself "odd".

Each time your hear "black" after that, change the parity: "even", "odd", ... etc.

When it's your turn, if the black hats you see match the running parity, you're Red; Black otherwise.

Call out your color.

Three guys walk into a hotel, and they're going to split the cost of a room. The room is $30. They each kick in $10 and head up to their room. The manager gets wind of it and tells the clerk the room is only $25. He hands five $1 bills to the bell hop and tells him to go refund the guys' money. On the way up to the room, the bell hop gets to thinking and says to himself, "No way can three guys split $5, I'm going to help out." He stuffs $2 in his pocket, knocks on the door, gives each guy back a buck and heads back downstairs to the desk, glowing in the warmth of a job well done. So now each guy has paid $9. $9 times 3 is $27 plus the two bell hop stole -- only $29! Where is the other buck?

Answer: It's an erroneous question. The calculation should be $27 minus two,

since each guy paid $9, and the cost of the rooms was $25,

leaving $2 for the bell hop.

A man is hiking up a snowy mountain. He comes across a cabin. Inside the cabin is a small fire and two dead man. How did they die? (They did not burn to death)

Answer: An aeroplane crashed into the mountain and the aeroplane cabin was what was left.

Mel Colly stared through the dirty soot-smeared window on the 26th floor of the office tower. Overcome with depression he slid the window open and jumped through it. It was a sheer drop to the ground. Miraculously after he landed he was completely unhurt. Since there was nothing to cushion his fall or slow his descent, how could he have survived?

Answer: He was a window cleaner and was on the outside of the window.

He jumped inside.

A pot of gold is on a square island surrounded by a chasm 10 metres wide and of infinite depth. You have two 9.8 metres poles. How do you get across to the pot of gold and get back with it?

Answer: Take one pole and lay it across the corner of the chasm

so each end of the pole is touching a different side of the chasm.

The middle of the pole will now be closer than 9.8 meteres to the island.

OR

Answer: Diagonal placement of poles in a T-like shape where the

top part of the T rests on part that's not the island.

You have three lights in a box, each of which is connected to a switch outside the box. The box is closed. You need to figure out which switch to corresponds to which light and you can open the box only once (and you can't manipulate the switches after you open the box). How do you do this?

Answer: Turn on a switch and leave it on for a while.

Then turn it off and turn another switch on.

Open the box.

Feel the lights - the warmest light corresponds to the switch that was first turned on for a while then off.

The light currently on corresponds to the switch that is currently on.

The remaining light and switch correspond to each other.