Mathematicians In A Bar
An infinite crowd of mathematicians enters a bar. The first one orders a pint, the second one orders a half pint, the third one orders a quarter pint, and so on.
The bartender interrupts, "I get it!" – then pours the order for all of the mathematicians. How many pints does the bartender pour?
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10 solutions
Discussions for this problem are now closed
Using the sum of a geometric series , the answer will be
1 + ( 1 / 2 ) + ( 1 / 4 ) + ( 1 / 8 ) + … = 1 − 2 1 1 = 2
Large bar he has.
The power of mathematics: something impossible made possible, something illogical made logical.
like how Larry can buy 48 watermelons and 68 cartons of milk and no one asks why XD
Mathematics is the product of our logic and reasoning, not the other way around. That above is not 'illogical', rather, it is logically impossible for them to order more than 2 pints (and what math did was it presented it in terms of numbers - simplifying the complex scenarios that exist in our minds).
Not necessarily. Maybe the first mathematician takes up 1 meter square, and the second takes up 1/2 meter square and the third takes up 1/4 meter square, .....
It becomes an issue if the third takes up 1/3 meter square though. Just saying.
Calvin, you hit on something that my calculus teacher of many years pointed out: the addition of physical objects to a word problem like this raises objections to the answer. If the question had concerned "a pint of bitter," at some point the fraction of a pint at the next step in the summation would be smaller than the size of the smallest molecule in the bitter, What then? (His example was: consider a trumpet made by rotating a segment of one branch of a hyperbola around its asymptote, letting it extend to infinity as it approaches that asymptote. The trumpet can be filled with a finite amount of paint, but it takes an infinite amount of paint to paint its exterior!
I don't get it because I added up 1 and a half and that's 1 1/2 and add the quarter that equals 1 1/2
@Demi Grant – Remember it is an infinite number of mathematicians and each one orders half of the previous one (not called out but assumed from the pattern). Each additional glass poured will be half as much as it would take to get to 2 pints. This is a classic limits problem (X approaches 2).
And very poor business when your clients are mathematicians....
Not really cause he will charge em all the full price ;-)
we ever discuss this somewhere ......
That's what she said.
I don't understand. The question is "How many pints,..."? And not how many beer! Then the final part (1/8) is wrong. Or not?
The thing is, it will never be 2 pints because the number of matematicians is infinite. And as it is infinite the divisions will also be, so it's impossible that the amount of beer can fill up to 2 pints. Please tell me if i'm wrong.
Didnt understand it.
Another way to see the solution would be the following: the infinite series mentioned in the problem can be described in the form of 1 + 1 / 2 + 1 / 4 + 1 / 8 + …
If we exclude the "1", which is the easiest part, we get a new infinite series, 1 / 2 + 1 / 4 + 1 / 8 + …
Then, we realize the following: 1 − 1 / 2 = 1 / 2 1 − ( 1 / 2 + 1 / 4 ) = 1 / 4 1 − ( 1 / 2 + 1 / 4 + 1 / 8 ) = 1 / 8
This can be formalized, but the pattern is that subtracting up to 2 n 1 gives 2 n 1 . Thus, subtracting up to ∞ gives (informally) 2 ∞ 1 = 0 . Thus, the sum must be equal to 1.
Given that the new series is the original series excluding the initial +1, the original series converges into 2.
In theory, the answer is 2. In reality, a point is reached were the total mass of beer required is smaller than a single atom. Thus, there is no more beer. The correct answer is it would take an infinite amount of beer.
Not really. It asks how much beer the bartender pours for the mathematicians to DIVIDE THEMSELVES. Basically the bartender is leaving the problem of splitting ingredients and molecules to the mathematicians. In the event they run into a roadblock he will have still poured only two pints.
You, Sir, have explained the highest up-voted answer in the most eloquent way! Thank you :)
Let x=1+1/2+1/4+1/8+....
Then 2x=2+1+1/2+1/4+...
X=2x-x.
X=2+1+1/2+1/4+...-(1+1/2+1/4+1/8+...)
=2
The bartender only needs to pour two pints. But technically should the answer be infinitely approaching two pints?
Obviously a barman who knows his limits
Let's say that the whole amount of drinks is x. Then 2 1 x is 1. Then x is 2. That's how I did it.
This particular problem can be solved in a different way ( rather than applying the formula for sum of infinite G.P) 1+1/2+1/4+...= 1+1-1/2+1/2-1/4+1/4-1/8..... =2
That's one of my favorite "bad" jokes.
As the joke goes, the bartender looks at the crowd of mathematicians, pours them only 2 pints, and says, "you need to know your limits".