Bruce is an inmate at a large prison, and like most of the other prisoners, he smokes cigarettes. During his time in the prison, Bruce finds that if he has 3 cigarette butts, he can cram them together and turn them into 1 full cigarette. Whenever he smokes a cigarette, it turns into a cigarette butt.
One day, Bruce is in his cell talking to one of his cellmates, Steve.
"I really want to smoke 5 cigarettes today, but all I have are these 10 cigarette butts," Bruce tells Steve. "I'm not sure that will be enough."
"Why don't you borrow some of Tom's cigarette butts?" asks Steve, pointing over to a small pile of cigarette butts on the bed of their third cellmate, Tom, who is out for the day on a community service project.
"I can't," Bruce says. "Tom always counts exactly how many cigarette butts are in his pile, and he'd probably kill me if he noticed that I had taken any."
However, after thinking for a while, Bruce figures out a way that he can smoke 5 cigarettes without angering Tom. What is his plan?

Bruce takes 9 of his 10 cigarette butts and turns them into 3 cigarettes total (remember, 3 cigarette butts can be turned into 1 cigarette). He smokes all three of these, and now he has 4 cigarette butts.
He then turns 3 of the 4 cigarette butts into another cigarette and smokes it. He has now smoked 4 cigarettes and has 2 cigarette butts.
For the final step, he goes and borrows one of Tom's cigarette butts. With this cigarette butt plus the 2 he already has, he is able to make his 5th cigarette to smoke. After smoking it, he is left with 1 cigarette butt, which he puts back in Tom's pile so that Tom won't find anything missing.

Consider the following explanation for why 1=2:
1. Start out Let y = x
2. Multiply through by x xy = x2
3. Subtract y2 from each side xy - y2 = x2 - y2
4. Factor each side y(x-y) = (x+y)(x-y)
5. Divide both sides by (x-y) y = x+y
6. Divide both sides by y y/y = x/y + y/y
7. And so... 1 = x/y + 1
8. Since x=y, x/y = 1 1 = 1 + 1
8. And so... 1 = 2
How is this possible?

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not followinng basic mathematical rules, we are able to get strange results like these.

It regulates our daily movements, but it feels no interest in our lives. It directs us when to come and go, but does not care if we pay attention. What is it?

There are 3 switches outside of a room, all in the 'off' setting. One of them controls a lightbulb inside the room, the other two do nothing.
You cannot see into the room, and once you open the door to the room, you cannot flip any of the switches any more.
Before going into the room, how would you flip the switches in order to be able to tell which switch controls the light bulb?

Flip the first switch and keep it flipped for five minutes. Then unflip it, and flip the second switch. Go into the room. If the lightbulb is off but warm, the first switch controls it. If the light is on, the second switch controls it. If the light is off and cool, the third switch controls it.

This is an unusual paragraph. I’m curious as to just how quickly you can find out what is so unusual about it. It looks so ordinary and plain that you would think nothing was wrong with it. In fact, nothing is wrong with it! It is highly unusual though. Study it and think about it, but you still may not find anything odd. But if you work at it a bit, you might find out. Try to do so without any coaching.

The letter "e", which is the most common letter in the English language, does not appear once in the long paragraph.

A man was driving a truck at 60 mph. He did not have his headlights on and the moon was not up. Yet he did not hit the woman who crossed the road. How?