A man puts on a clean shirt every night before bed. On the first nigh he puts on a blue shirt. He than sleeps for 5 hours. Every one hour more he sleeps than the night before he put on a different color shirt the next night according to this scale: blue, black, red, green, white, pink, orange, brown, purple, yellow, grey, neon green, tan, and teal. Every one hour less he sleeps than the last night he put on a different color shirt the next night going backwards on his scale.
If he were to wear a blue shirt because he slept more hours than the last night he does. If it was because he slept less hours than the night before he skips it and wears a teal shirt instead. If he goes backwards on the scale and goes to blue but would not wear a blue shirt he still counts blue in his going backwards on his scale.
The second night the man wears a blue shirt because he did not sleep any more or less hours than the last night. The man sleeps for six hours that night.
The next night he sleeps for five hours.
Night number four he sleeps for eight hours.
The next night he sleeps for seven hours.
The next night he sleeps so well he sleeps for 11 hours.
Night number seven he stays up so late he only sleeps for four hours.
The next night he is so tired he sleeps for eight hours.
The next night he sleeps for eight hours again.
Night number ten he sleeps for 14 hours because he is sick.
Since he slept so long the last night he only sleeps for seven hours.
The next night he is a little bit tired so he sleeps for eight hours.
The night after that he had to do so much work he only slept five hours.
The next night at work they let him out early and he slept for nine hours.
The next night he slept for eight hours.
And the last night the man did he slept for ten hours.
The next night he put on a different color shirt according to his scale, but the next night he randomly picked a shirt. At what night will the man wear a blue shirt again?

Emily was sitting at her study table, home alone, on a cold and stormy night. Her parents had taken a flight earlier in the morning to Australia as her grandmother had passed away. She had wanted to follow her parents but she had an important English examination the next day which she could not miss. The storm was getting heavier by the minute and the wind was howling outside. All this noise made it very hard for her to concentrate. She was on the verge of dozing off when she was shaken alert by a sudden "THUD!" She dismissed it as a window which had been slammed shut by the wind.
She tried to concentrate on her books when she heard faint footsteps. Emily got out of her room and looked around when suddenly, without warning, she was grabbed by the neck. She tried to scream but it came out as a mere whimper as the intruder was pressing hard against her throat with his arm. She tried to free herself from his grip but to no avail.
"Give me all your money!" growled the man who had grabbed her from behind.
"Th-there is none h-here! Please ll-let me go!" cried Emily.
"Don't LIE TO ME!" screamed the increasingly agitated man. She felt the man strengthen his grip around her neck. She said nothing and a few seconds passed by in silence. Suddenly the phone rang which alerted both of them.
"People will get suspicious if I don't answer the phone," said Emily, with a controlled voice. The intruder let her go.
"Alright, but NO funny business, or ELSE!" said the nervous intruder. Emily walked toward the phone. She took a deep breath and calmed herself. She picked up the phone. "Hey Em! How's the revision going?" said the caller.
"Hey Anna. Thanks for the call. Hey you know those Science notes I lent you last week? Well I really need them back. It would be a great help to me. It's an emergency, so if you could give me them tomorrow it would be great. Please hurry in finding the notes. I need to get back to my books now. Bye," Emily said. She hung up the phone.
"It was wise of you not to say anything," said the intruder, although he was more than a bit confused by her conversation.
"Now TELL ME WHERE THE MONEY IS KEPT!" screamed the thief.
"It...it's...in my dad's room. The first room on the right. Third drawer," said Emily. "SHOW me!" said the man, and removed his grip around her neck. She took a big gulp of air and nearly fell. She swallowed hard and said a silent prayer. She walked slowly, in silence, toward her father's room. All of a sudden, they heard police sirens. The intruder froze in his footsteps. He ran to the nearest window and jumped out of it. Emily ran outside in time to see the intruder being escorted into the car. She saw Anna and she ran toward her and hugged her.
"Smart kids," said the policeman.
What had happened?

Emily had used the mute button during her conversation with Anna so that all Anna heard was: "call...help...emergency...please hurry".
Anna, sensing something was wrong, called the police and told them Emily's address. The police were able to come to Emily's house in time to catch the perpetrator.

A man has two ropes of varying thickness (Those two ropes are not identical, they aren’t the same density nor the same length nor the same width). Each rope burns in 60 minutes. He actually wants to measure 45 mins. How can he measure 45 mins using only these two ropes.
He can’t cut the one rope in half because the ropes are non-homogeneous and he can’t be sure how long it will burn.

He will burn one of the rope at both the ends and the second rope at one end. After half an hour, the first one burns completely and at this point of time, he will burn the other end of the second rope so now it will take 15 mins more to completely burn. so total time is 30+15 i.e. 45mins.

Two trains are traveling toward each other on the same track, each at 60 miles per hour. When they are exactly 120 miles apart, a fly takes off from the front of one of the trains, flying toward the other train at a constant rate of 100 miles per hour. When the fly reaches the other train, it instantly changes directions and starts flying toward the other train, still at 100 miles per hour. It keeps doing this back and forth until the trains finally collide.
If you add up all the distances back and forth that the fly has travelled, how much total distance has the fly travelled when the trains finally collide?

The fly has travelled exactly 100 miles. We can figure this out using some simple math. Becuase the trains are 120 miles apart when the fly takes off, and are travelling at 60 mph each, they will collide in exactly 1 hour. This gives the fly exactly 1 hour of flying time, going at a speed of 100 miles per hour. Thus, the fly will travel 100 miles in this hour.

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

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.

There are 1 million closed school lockers in a row, labeled 1 through 1,000,000.
You first go through and flip every locker open.
Then you go through and flip every other locker (locker 2, 4, 6, etc...). When you're done, all the even-numbered lockers are closed.
You then go through and flip every third locker (3, 6, 9, etc...). "Flipping" mean you open it if it's closed, and close it if it's open. For example, as you go through this time, you close locker 3 (because it was still open after the previous run through), but you open locker 6, since you had closed it in the previous run through.
Then you go through and flip every fourth locker (4, 8, 12, etc...), then every fifth locker (5, 10, 15, etc...), then every sixth locker (6, 12, 18, etc...) and so on. At the end, you're going through and flipping every 999,998th locker (which is just locker 999,998), then every 999,999th locker (which is just locker 999,999), and finally, every 1,000,000th locker (which is just locker 1,000,000).
At the end of this, is locker 1,000,000 open or closed?

Locker 1,000,000 will be open.
If you think about it, the number of times that each locker is flipped is equal to the number of factors it has. For example, locker 12 has factors 1, 2, 3, 4, 6, and 12, and will thus be flipped 6 times (it will end be flipped when you flip every one, every 2nd, every 3rd, every 4th, every 6th, and every 12th locker). It will end up closed, since flipping an even number of times will return it to its starting position. You can see that if a locker number has an even number of factors, it will end up closed. If it has an odd number of factors, it will end up open.
As it turns out, the only types of numbers that have an odd number of factors are squares. This is because factors come in pairs, and for squares, one of those pairs is the square root, which is duplicated and thus doesn't count twice as a factor. For example, 12's factors are 1 x 12, 2 x 6, and 3 x 4 (6 total factors). On the other hand, 16's factors are 1 x 16, 2 x 8, and 4 x 4 (5 total factors).
So lockers 1, 4, 9, 16, 25, etc... will all be open. Since 1,000,000 is a square number (1000 x 1000), it will be open as well.

One day, Emperor Akbar posed a question to Birbal. He asked him what Birbal would choose if he offered either justice or a gold coin.
"The gold coin," said Birbal without hesitation.
On hearing this, Akbar was taken aback. "You would prefer a gold coin to justice?" he asked, not believing his own ears.
"Yes," said Birbal.
The other courtiers were amazed by Birbal's display of idiocy. They were full of glee that Birbal had finally managed himself to do what these courtiers had not been able to do for a long time - discredit Birbal in the emperor's eyes!
"I would have been disappointed if this was the choice made even by my lowliest of servants," continued the emperor. "But coming from you it's not only disappointing, but shocking and sad. I did not know you were so debased!"
How did Birbal justify his answer to the enraged and hurt Emperor?

"One asks for what one does not have, Your Majesty." said Birbal, smiling gently and in quiet tones.
"Under Your Majesty´s rule, justice is available to everybody. But I am a spendthrift and always short of money and therefore I said I would choose the gold coin."
The answer immensely pleased the emperor and respect for Birbal was once again restored in the emperor's eyes.

I know a number which when multiplied by multiple of 9 i.e 9 18 27 36 45 ... The output consist of number containing only one digit.
Can you identify the number?