Ok. I found this at another message board. I am willing to admit that there is a good possibility that I am just a dolt and the answer is right in front of my face but I can’t seem to find it. I haven’t changed anything about this post (even the spelling ::shudder::. That was hard for me to ignore) just incase there are any mess ups in the equation that I’m missing. You can be honest. Am I totally oblivious or is this really as mind bending as it seems to be for me?
"“The Missing Dollar”
Three man walk into a Pizzaria and order a Large Pizza each. Large pizzas sell for $10 here. So the men men each pay their $10 for their pizzas. thats $30 in total.
The three men go and sit down and the waiter goes to put their sale through the register. The boss stops him and reminds the waiter that they are having a special on three pizzas at the moment. Three large Pizzas for $25. So he tells the waiter to give the men $5 change.
The waiter realises that $5 can’t be split three ways so he decides to only give them $3 change and keep the other $2. He gives each man $1 and puts the other $2 in his Pocket.
What am I talking about here? Well lets add it all up now.
The three men Spent $10 each ($30), but got a dollar back. So they spent $9 each ($27). And the Waiter pocketed $2.
$27 + $2 = $29
Wheres the other dollar gone?
Again?
They spend $30
They should get $5 change, but only get $3 and the Waiter takes $2.
Meaning they only spent $27 and the Waiter has $2. It only equals $29
It’s a paradox found in mathematics. I’m not sure what this means but usually when they find a paradox within a scientific theory they later find many othe flaws in the same theory.
This is an ancient brain teaser; it is usually told with three guests sharing a room at a hotel, and the bellhop pocketing the extra two bucks.
The best way to attack this is to see where the actual currency is. The cash register initially got $30, but then five dollars was removed, leaving $25 in the register. The five bucks is divided $1 for each purchaser and $2 for the waiter. ll the actual cash is accounted for
The paradox in the problem as stated is that the teller is slyly equating dollars paid ($27) with dollars held (the waiter’s $2). The key is realizing the men may have paid a net of $27, but two of these dollars actually went to the waiter; the other $25 are still in the register.
It hasn’t gone anywhere. Initially, they spent 30, but they got 3 back – so they actually spent 27. 25 of that went to the pizza place, and 2 to the waiter.
restaurant gets 30
men should get 5 back
waiter takes 5 dollars from the 30, gives men only 3, keeps 2 for himself
= men pay 2 dollars extra, that 2 dollars going into the waiters pocket, but restaurant gets 25 as it should.
Just in case it’s still not clear, I might as well throw in one more explanation – basically the same, phrased slightly differently.
First of all, the $2 received by the waiter is included in the $27 the men spent. They gave $30, they got back $3, and 2 of the remaining $27 dollars were kept by the waiter (with the other 25 being kept by the pizza place.)
So really, the only question you could ask was “Where are the other three dollars.” (Again, you can’t add the $2 to the $27 because the $2 were included in the $27).
The answer: The other three dollars were given back to the three men.
I didn’t think it was a paradox either. I just figured there was some way I wasn’t perceiving it or something that I was missing that was inhibiting my brain from getting a firm grasp on it. Thanks guys!
[… Meaning they only spent $27 and the Waiter has $2.]
Actually, everything is fine up to here. So the three men spent $27, with $25 in the cash register and $2 in the waiter’s pocket.