### #1 - Classic Logical Interview Puzzle

I have two rectangular wires.
Both of them have property that when i light the fire from one end , it will take 60 minutes to get completely burn.
However they do not burn at consistent speed (i.e it might be possible 1st 20% burn in 50 minutes and 80% can burn in 10 minutes).

So how could i measure 45 minutes ?

Steps:
A) burn 1st wire from both end and 2nd wire from one end
B) After 30 minutes(when 1st wire gets completely burned out) , burn the second wire from 2nd end as well
C) when 2nd run completely gets burned , you know its 45 minutes.

### #2 - Logic Problem Puzzle

A donkey travels the exact same distance daily.
strangely 2 of his legs travels 40 kilometers and the remaining two travels 41 kilometers.
Obviously 2 donkey legs cannot be a 1km ahead of the other 2.

The donkey is perfectly normal. So how come this be true ?

The donkey is moving in circular path and hence outside legs travels more distance than inner legs

### #3 - Marbles Puzzle

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box ?

There are 3 marbles (1 blue, 1 green, and 1 red).

### #4 - Tricky Logical Mind Bender

A man was gazing through the window of the 33rd floor of the building. He suddenly opened the window and jumped on the other side of the window. On landing the floor, there was not a sheer mark of injury on him.

How can that be possible if he did not use any kind of parachute and did not land on a soft surface ?

The man is a window cleaner who jumped inside of the window after finishing off on the 33rd floor.

### #5 - Water Pails Puzzle

If you had an infinite supply of water and a 5 quart and 3 quart pails, how would you measure exactly 4 quarts? and What is the least number of steps you need?

1. Fill 5 quarter pill ( 5p - 5, 3p - 0)
2. Transfer to 3 quart pail (5p - 2, 3p - 3)
3. Empty 3 quarter pill ( 5p - 2, 3p - 0)
4. Transfer 2q from 5 pail to 3 pail (5p - 0, 3p - 2)
5. Fill 5 quarter pail(5p - 5, 3p - 2)
6. Transfer 1q from 5 pail to 3 pail(5p - 4, 3p - 3)

### #6 - Maths Classic Race Puzzle

Lavesh, Bolt, and Lewis race each other in a 100 meters race. All of them run at a constant speed throughout the race.

Lavesh beats Bolt by 20 meters.
Bolt beats Lewis by 20 meters.

How many meters does Lavesh beat Lewis by ?

Lavesh beats Lewis by 36 meters.

It is tempting to guess that Lavesh beats Lewis by 40 meters, but when Lavesh finishes and is 20 meters ahead of Bolt, Bolt is NOT 20 meters ahead of Lewis (he's only 16 meters ahead), and it will take a couple more seconds before Bolt increases his lead over Lewis to 20 meters.

To figure out the answer, we let Lavesh's speed be A meter/second. So it takes him 100/A seconds to finish the race. At this point, we know that Bolt has run 80 meters (since Lavesh beats him by 20 meters). So Bolt runs 80 meters in 100/A seconds, meaning that he is running at a speed of (80/(100/A)) meters/second, or (8A/10) meters per second.

So we then know that it takes Bolt 100/(8A/10) seconds to finish the race, or 125/A seconds. At this point, we know that Lewis has run 80 meters (since Bolt beats him by 20 meters). So Lewis runs 80 meters in 125/A seconds, meaning that he is running at a speed of (80/(125/A)) meters/second, or 80A/125 meters per second.

Now that we know Lewis's speed, we just need to figure out how far he had run when Lavesh finished the race. Since Lavesh finished in 100/A seconds, we can determine that Lewis had run (100/A) * (80A/125) = 8000/125 = 64 meters when Lavesh finished the race. And so Lavesh beat him by (100 - 64) = 36 meters.

### #7 - Morgan Stanley Induction Logic Interview

The wisest men of the kingdom are called upon by the king to his court. One of them is to be chose for the advisor rank and thus they shall prove their worth in the test. The king places hat on each of their hats. Each one of them can see other two hats but can't see his own. The hats are either white or black.

For a hint, the king tells them that at least one of them is wearing a black hat. Also the king declares that the test is totally fair for each one of them. Now the first one from them who is able to deduce the color of hat he is wearing will be designated as the advisor. After a few minutes, one of them was able to deduce the color of his own hat. How ?

Suppose that there is just one black hat. In such a scenario, the person wearing it will see the other two hats as white and then as the king had announced, he will be easily able to judge that he is wearing a black hat himself. But the other two men will see a black hat and a white hat and will not be able to judge. Thus this will be an unfair situation, so we can rule it out.

Now suppose that there are two black hats. Then, both the person will see a white hat and a black hat. And they have already realized that there must be two black hats, thus they can easily deduce that they are also wearing a black hat. But the one wearing white hat will see two black hats and thus he will not be able to identify on a sure note. Thus the competition will not be fair.

Thus the only situation where the competition can be fair is when all the hats are black. The first one who recognize the fact will stand up and say black.

### #8 - Monty Hall Problem Puzzle

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

You better switch!

Your first choice has a 1/3 chance of having the car, and that does not change.
The other two doors HAD a combined chance of 2/3, but now a Goat has ben revealed behind one, all the 2/3 chance is with the other door.