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August 11, 2011

A revolver with 2 bullets

You have been taken hostage by terrorists. Terrorist has a revolver with 6 empty chambers. He now loads the revolver with 2 bullets in front of you. These two bullets are kept next to each other (contiguously) in the 2 adjacent chambers, the terrorist now spins the barrel so that now you don't know what is location of bullets in chamber. He keep the revolver against your head and pulls the trigger. But its lucky day for you. It was the empty chamber. Now terrorist gives a slight chance to get free. He gives you a choice whether he should spin the barrel first then pull the trigger again.. or should just simply pull the trigger again ? If you get lucky again, terrorists will let you go..otherwise ..!!!

So what would you prefer ? Would you want him to spin the barrel first then shoot or just shoot without spinning the barrel ?


Tiger Woods said...

You want him to shoot again without spinning the barrel. This gives you a 75% chance of living, versus a 66.67% chance if you let him spin the barrel before shooting again.

The key phrase in this brain teaser is that the bullets are loaded next to each other in adjacent chambers and aren't randomly placed in the revolver.

DonFriend said...

how please explain

subliminal said...

I blindfold you and place 20 playing cards in front of you. I tell you that 5 of the playing cards are face up and challenge you to divide the 20 cards into 2 piles so that there are the same number of cards face up in each pile. How do you do it?

Unknown said...

Divide the 20 cards into piles of 15 and 5.Then flip the all the cards in the smaller pile(5 cards). Now the number of cards face up in each pile is same.

Dogtag114 said...

B B - Dead Already
BB - Dead Already

F = First Shot
B = Bullet
E = Empty

First Shot = Empty, eliminates two options
Second Shot without spinning, 3/4 are empty = 75% empty
Second Shot with spinning, 4 of 6 are empty = 66.6% empty

Dogtag114 said...

Wait... My table format looked bad and I think I forgot that there is a just an empty shell still in one of the chambers that would still not kill you. Therefor if you spin again, odds are only 1/6 that you get a fireable bullet.

I change my answer to spin.

Dogtag114 said...

Last post for me... ignore the previous post... a few glasses of wine...

The proper solution:

BEEEEB - Dead Already
BBEEEE - Dead Already

B = Bullet
E = Empty

First Shot = Empty, eliminates two options, the sample space is now 4

Second Shot without spinning, 3/4 are empty = 75% to live

Second Shot with spinning brings all six possibilities back in play and now 4 of 6 are empty = 66.6% to live

Better to not spin.

Jason Kline said...

You should spin. If you don't spin, there are 3 empty chambers and 2 loaded chambers. 3/5 = 60% chance of survival.

If you do spin, there are 4/6 empty chambers, which equals 66 1/3% chance of survival.


Mcguinnen said...

The real question is:

Do I feel lucky? Well do you, Punk?

There is no real right or wrong answer for this one, its not really a logic or math question, its more of a
"take a side" question.

Anyway this is a gamble and gambling is all about odds, odds which are mathematically probable but never reliable. Like a roulette wheel.

I personally wouldn't want to give satisfaction to the terrorist for answering his retarded riddle. But that's the side I choose.

"Do what you like asshole" I'd say because I'd be aiming to kick him in the balls about then.

AlexStar6 said...

Spin the Barrel. It might seem like this is a math problem but it's not, it's a physics one. Actually physics testing on the game of "Russian Roulette" show that the likely hood of the full chamber being the first round fired is negligible with only one bullet in the chamber and rises incrementally as you add bullets. The reason for this?


The weight of a bullet in the chamber will cause that chamber to find a resting point at the bottom of the spin, thus leaving an empty chamber at the top.

Anonymous said...

I agree with AlexStar6. But I like McGuinnen's answer XD. I would tell the guy to shoot. Either way if you dont die from the shot and you are bad at physics, the guy is a terrorist, he's going to kill you anyways, he's just trying to get your hopes up of being free.

Anonymous said...

@Mcguinnen: Clint Eastwood in Dirty Harry, not John Wayne.

@JasonKline: Don't spin. There are 2 loaded chambers, but since you are alive, you didn't get either of those. So the question is which empty one did you get? The empty one with the loaded one next is the only one that gets you. So given that you are alive, there is a 25% that there is a bullet in the chamber. Spin & there is a 33% chance that there is a bullet in the chamber.

Anonymous said...

When he shot the first time the odds were 2/3 u got an empty chamber(66.66%). Afterwards the odds are now 3/5 (60%) chance of ur safety. If the barrel is re-spun the odds return to the 2/3 chance. While the odds only increase 6.66% ,I'd rather have even slightly better ods working for me.

Now to comment on the situational dynamic:

Are we certain that givent this guys mental state,can we trust him to end things here and now?(in otherwords he plays the game this one last time and ur safe thereafter).

As long as there is a momentary pause between the first and second time the gun is at ur head(he spins the chambers away from ur head) I'd be tempted to take that moment to punch him hard and take him down fast. Assuming I was not shaking like a leaf at the time.

John said...

Tiger is correct.

no spin, consecutive chambers must be empty.
P(e1|e2)=P(e1 and e2)/P(e1)=(3/6)/(4/6)=.75

P(e2) = 4/6 = .66