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shalini_goel14 • Jun 5, 2009

# Where is the remaining 1 buck?

Hi All,

Anyone here know the answer of the folowing old puzzle. I could never know its answer.

Three friends went to a hotel. The bill was 75 bucks .Each one contributed 25 bucks. The waiter took the bill to the cashier.

The cashier was happy & decided to give them a discount of 5 bucks & asked the waiter to return them 5 bucks. Now the waiter was confused. How to distribute 5 bucks among 3 persons? He kept 2 bucks in his pocket & gave one buck to each one of the 3 persons.

So initially each one had contributed 25 bucks. Now as they are given 1 buck back, their contribution reduces to 24 bucks.

They all contributed 24 bucks--> that is 24x3=72 & 2 bucks are in the waiters pocket. The total becomes 74. But they had paid 75 bucks.
Where is the remaining 1 buck?.

Thanks a lot for answering !
sarveshgupta • Jun 5, 2009
the solution is as follows:

75 - 5 = 70

each paid 25

25-1 as they get 1 back = 24

that means according to them they paid 72

but 2 were with the waiter so 72 - 2 = 70 thats the actual room rent

so there is a calculation mistake instead of adding they have to subtract 2 from 72

Am i right?
shalini_goel14 • Jun 5, 2009
Hey sarvesh,

can you please explain why that 2 is subtracted and man initial amount was 75 so after totalling everything it should sum up to 75 not 70. Please make clear.

sarveshgupta • Jun 6, 2009
@shalini: i am telling you that only

we have to make total room rent of 75 initially

but now you can see the rent after the discount is 70

so we have to now prove the total to be 70 and not 75

it is just to confuse that the total is being tried to make it to 75 in the question

but if you see it clearly you will be able to understand it..

Am I clear?
silverscorpion • Jun 6, 2009
Well, as Sarvesh explained, it's all a mistake in calculation.

The total money given was 75 bucks, and each one received one buck back..
So, the total money spent was 72 bucks. Which should be equal to 70 plus 2.
70 bucks were received by the cashier, and 2 bucks were taken by waiter making a
total of 72. With the 3 bucks with the customers, the total comes to 75. Correct?

Am I clear??
silverscorpion • Jun 6, 2009
The mistake you are doing is that, you should subtract the 2 bucks from 72. Not add it.

You should make the total to 70, as i already said. So, 72-2 gives 70.

You added them, so, 72+2 gives 74. Giving you an illusion of one buck lost.

Hope the doubt is cleared.
Munguti • Jun 6, 2009
I agree with silverscorpion.
Another way of looking at it is from the spenders point of view which makes it very easy. According to the three men the both spent 24x3 which gives you 72.(It must be remebered here that the 2 bucks the waiter took is part of the 72 spent by the customers) the the three bucks that were returned to them making it 75. 😁
It's not that it was easy it's just that i am that good😎
skipper • Jun 6, 2009
There's a math puzzle in a section of one of the issues of SciAm I collected over the years, it discusses a problem like this, using the number 1 to add or subtract an 'extra' guest, rental, camel, whatever when an even/odd situation exists or there are an odd number of "guests, rooms, waiters, camels" etc to share between an even/odd number.

Adding an extra 1 or 2, so you even up (or make odd) the total to be shared out, resolves the repeating fraction dilemma. The addition is temporary, after sharing out the money, camels, whatever, there is 1 whole camel/dollar/slave/banana left over, or there are 2 left over.

1 and 2 are like placeholders for a binary (or trinary etc) algorithm that partitions a total oddly or evenly.

I might just initiate a search for that mag, but I have quite a stack so can't say if the search algorithm will halt.
kashish0711 • Jun 7, 2009
lolz finally got it.
This maths really amazies me. n_n
shalini_goel14 • Jun 7, 2009
silverscorpion
Well, as Sarvesh explained, it's all a mistake in calculation.

The total money given was 75 bucks, and each one received one buck back..
So, the total money spent was 72 bucks. Which should be equal to 70 plus 2.
70 bucks were received by the cashier, and 2 bucks were taken by waiter making a
total of 72. With the 3 bucks with the customers, the total comes to 75. Correct?

Am I clear??
Oh yes, Now i got it . Thanks a lot sarvesh and Scorpion. 😁 Total money spent should be 72 not 75.