Find the odd ball from twelve balls puzzle

There are 12 balls. 11 of the balls weigh the same.
1 of the balls is either heavier or lighter than the rest.
You have an unmarked balance scale.
Using the scale only 3 times, determine which ball is different and whether it is heavier or lighter than the rest.

Russian roulette interview puzzle

"Let's play a game of Russian roulette," begins one interview stunt that is going the rounds at Wall Street investment banks. "You are tied to your chair and can't get up. Here's a gun. Here's the barrel of the gun, six chambers, all empty. Now watch me as I put two bullets in the gun. See how I put them in two adjacent chambers? I close the barrel and spin it. I put the gun to your head and pull the trigger. Click. You're still alive. Lucky you! Now, before we discuss your résumé", I'm going to pull the trigger one more time. Which would you prefer, that I spin the barrel first, or that I just pull the trigger?" 

The good news is that the gun is imaginary. It's an "air gun," and the interviewer makes the appropriate gestures of spinning the barrel and pulling the trigger. The bad news is that your career future is being decided by someone who plays with imaginary guns. This question is a logic puzzle. It has a correct answer, and the interviewer knows what it is. You had better supply the right answer if you want the job. 

In the context of a job interview, solving a puzzle like this is probably as much about stress management as deductive logic. The Russian roulette question exemplifies the mind-set of these interviews - that people who can solve puzzles under stress make better employees than those who can't. The popularity of today's stress- and puzzle-intensive interviews is generally attributed to one of America's most successful and ambivalently regarded corporations, Microsoft.

High School Locker Puzzle

A high school has this ritual on the last day of school:
The students go into the hall and stand by their closed lockers.

At the first blow of a whistle, the students open every locker.
At the second whistle, the students close every second locker (lockers 2,4,6, etc., are slammed shut).
At the third whistle, the students toggle every third locker.
To "toggle" means to close it if it's open, and to open it if it's closed. They toggle lockers 3,6,9, etc.

At whistle four, they toggle every fourth locker. They toggle lockers 4,8,12, etc.
At whistle five, they toggle every fifth locker, and so on.

Let's make things easy and say it's a small school with only 100 lockers.
At the one hundredth whistle, the student standing next to locker 100 (and only that student) toggles his locker.
How many lockers are then open?

Measure time with burning fuse puzzle

You have two lengths of fuse. Each will burn for exactly one hour.

But the fuses are not necessarily identical and do not burn at a constant rate.

If half the fuse is burnt, then it does not mean that it had burnt for 30 minutes.

There are fast-burning sections and slow-burning sections, on the whole length of the fuse.

How do you measure thirty minutes using only the fuses and a lighter?

How do you measure forty-five minutes using only the fuses and a lighter?

Fifty red and fifty blue marbles probability puzzle

You have two jars and hundred marbles.

Fifty of the marbles are red, and fifty are blue.

You must place all 100 marbles in the jars.

You can decide how many and what marbles to be placed in each of the jars.
Each jar can hold 100 marbles.
One of the jars will be chosen at random; then 1 marble will be withdrawn from that jar at random.

How do you maximize the chance that a red marble will be chosen?

What is the chance of selecting a red marble when using your scheme?

4 people must cross a rickety bridge in 17 minutes

Four people must cross a rickety footbridge at night.
Many planks are missing, and the bridge can hold only two people at a time (any more than two, and the bridge collapses).
The travelers must use a flashlight to guide their steps; otherwise they're sure to step through a missing space and fall to their death. There is only one flashlight.
The four people each travel at different speeds.
Adam can cross the bridge in one minute; Larry in two minutes; Edge takes five minutes; and the slowest person, Bono, needs ten minutes.
The bridge is going to collapse in exactly seventeen minutes.
How can all four people cross the bridge?

Five Jar of Pills and Scale Puzzle

You have five jars of pills. All the pills in one jar only are "contaminated."

The only way to tell which pills are contaminated is by weight.
A regular pill weighs 10 grams; a contaminated pill is 9 grams.
You are given a scale and allowed to make just one measurement with it.
How do you tell which jar is contaminated?