### Brain Teasers

# Math Magicians

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?

### Answer

Just 1. Add 'em up!Hide Answer Show Answer

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## Comments

It's a very tiny bit lesser than 1.

1/2+1/4+1/8+1/16+1/32+1/64+1/128

No matter how much we add up, they always will be lesser than 1. I hope you get what I mean.

1/2+1/4+1/8+1/16+1/32+1/64+1/128

No matter how much we add up, they always will be lesser than 1. I hope you get what I mean.

Yes, good point - but technically, the answer is still one. If you just keep adding up 1/2+1/4+1/8+1/16.... and don't stop adding, the gap between one and the answer will get "infinitely small," and since infinity is an undefinable number that goes on forever, there is essentially no gap between the answer and one. Check here: http://en.wikipedia.org/wiki/ 1/2_%2B_1/4_%2B_ 1/8_%2B_1/16_%2B_%C2%B7_%C2%B7_%C2%B7

Kinda how 0.999999... =1.

Sorry, but that is incorrect. It approaches 1, but never reaches 1. That is like saying 1/1.0E100 = 0 (since it is very, very close to 0). But if you multiply both sides by 1.0E100, then you get 1=0. Obviously, that is not a true statement. If you plot y=1/x on a graph, you will see that as x gets smaller, it approaches the y axis, but it will never, ever reach it.

It is correct! Take an integral and you get one!

Wolfpack and Yjunie, you need to take calculus. Also, read about Xeno's paradox. Yes, Achilles DOES catch the tortoise, 0.999... DOES exactly equal 1, as does the sum as n goes from 1 to infinity of 1 / 2^n.

To paraphrase Xeno, imagine yourself walking to your calculus class. At some point, you'll be half way there. At a later point, you'll be half of what's remaining. At a later point, you'll be half of what's remaining. In fact, you could describe your whole trip as the infinite sum. And guess what? You'll actually get there!!

To paraphrase Xeno, imagine yourself walking to your calculus class. At some point, you'll be half way there. At a later point, you'll be half of what's remaining. At a later point, you'll be half of what's remaining. In fact, you could describe your whole trip as the infinite sum. And guess what? You'll actually get there!!

Apart from the mathematical points being debated, this is in the wrong category. It is genuine math, not a trick!

He doesn't even need one. He needs thenumberthatisinfinetelyclosetoonebutnotone pints.

If I calculated, the answer will be 0.9999999999999999999...... And nobody would take that little amount away to give to their customers, so common sense, we will round it up to 1.(I'm referring to those stingy bartenders.)

Gbdf,, 0.9 recurring is equal to one - not 'a tiny bit less'. Consider this:

Let x = 0.9rec

Then 10x = 9.9rec

(10x - x) = (9.9rec - 0.9rec)

So 9x = 9 (the recurring decimals cancel off exactly)

Therefore 0.9rec = x = 1

A finite number of 9s - however large - after the decimal point is always a tiny bit less than 1. An infinite number of 9s closes the gap.

Of course in this teaser, the barman would not have to pour any beer, as he would die of old age before he'd taken everyone's order. ;)

Let x = 0.9rec

Then 10x = 9.9rec

(10x - x) = (9.9rec - 0.9rec)

So 9x = 9 (the recurring decimals cancel off exactly)

Therefore 0.9rec = x = 1

A finite number of 9s - however large - after the decimal point is always a tiny bit less than 1. An infinite number of 9s closes the gap.

Of course in this teaser, the barman would not have to pour any beer, as he would die of old age before he'd taken everyone's order. ;)

Nice! I found this one quite easy. It's a fun one, though.

Shouldn't this be Maths?

Agreed, if there are infinite mathmeticians the answer will always be less than 1.

No, Leadsinger, exactly 1. See my explanation above.

Forget all the math. At a certain point a single drop of beer would be too great for the fractional amount requested, so technically he A) could no longer fulfill the requests or B) if he continued giving the smallest amount of beer, a drop, then he would need an infinite number of pints because they never stop coming.

All in all, I thought it was a cute way to get people to think about the math of it (which can be hard to do), so good work!

All in all, I thought it was a cute way to get people to think about the math of it (which can be hard to do), so good work!

Doesn't matter whether it's one or slightly less than one, he'd just use one, because it would pretty hard to find 0.999... pint.

I love this one. My dad tells me this one all the time. He is a math teacher

i feel so stupid.

Since it was it "Trick" category I thought the answer is "0" because he never pours a whole pint.

But mathematically, I agree, the answer is 1

here is another proof, let x = number of pints

x = 1/2 + 1/4 + 1/8 + 1/16....

Multiply both sides by 2

2x = 1 + 1/2 + 1/4 + 1/8 + ....

2x = 1 + ( 1/2 + 1/4 + 1/8 + ...)

so we can replace whats in these brackets with "x"

2 = 1 + x

therefore,

x = 1

Cheers!

But mathematically, I agree, the answer is 1

here is another proof, let x = number of pints

x = 1/2 + 1/4 + 1/8 + 1/16....

Multiply both sides by 2

2x = 1 + 1/2 + 1/4 + 1/8 + ....

2x = 1 + ( 1/2 + 1/4 + 1/8 + ...)

so we can replace whats in these brackets with "x"

2 = 1 + x

therefore,

x = 1

Cheers!

This belongs in the math category. There is no trick here.

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