Monday, November 09, 2009

mystery discount



So these three guys go have lunch together and order the same item.  Everybody puts in $10.00 and gives it to the waiter.  He goes back to the cash register with the $30.00 and the manager tells him, "Oh, there is a special today their bill will only be $25 so give them $5.00 back.
Now the waiter is thinking $5.00 split three ways will be a problem so he pockets $2 and gives each customer $1.00.
So to summarize:
Each of the customers (3) paid $9.00 = subtotal $27.00
The waiter has $2.00 in his pocket
grand total $27 + $2 = $29

Where did the missing dollar go?

I think Bernie Madoff got it.

I wonder if Bernie used this type of accounting on those statements he gave out to his clients sucker victims.
My dad loved to tell this puzzle.  I think he really liked my reaction because starting in high school I really enjoyed math and started taking courses he never had.  He enjoyed the frustration the puzzle gave me.  He also enjoyed beating me in cribbage and counting the points faster than I could.  There's much more to math than arithmetic which I didn't care much about.
The reason I recall this puzzle is because I just found it in a book titled, "100 essential things you didn't know you didn't know".  It has 100 examples (2-3 pages each) of math usage.
One problem with this puzzle today is finding a $10.00 lunch at a restaurant with a wait staff.  That's harder than finding the missing dollar.  So here's an updated version with more money missing:

3 guys stop in a coffee shop and order similar drinks.  As in the other version, they each give the waiter $10.  As the waiter enters the items, he discovers the menu didn't show the new discounted prices and the total comes out to $23.00.  Like in the other story, he doesn't want the confusion of dividing the change and decides to take a little.  He pockets $1.00 and gives each customer $2.00.
Let's summarize:
3 guys paid $8 each = subtotal $24.00
waiter has $1 in his pocket
grand total $24 + $1 = $25
Now we are missing $5.00 and who's on first.

Maybe I could get an accounting job.
(if you are really wanting to know I'll put an answer in the comments later - so check back)

6 comments:

yorksnbeans said...

Well, the first scenario you need to divide the $28.00 by three if the waiter only took $2.00

The second scenario is not taking into account the full $30.00 that he was paid, only $25.00.

Unknown Mami said...

What about tax?

lisleman said...

@yorksnbeans - in a day or so I'll write a comment explaining the problem. I don't think dividing 28 by three makes any sense because the guys got that 3 dollars back. more later.
@unknown mami - you know, I was thinking of making a comment about taxes in the this story but that's not part of the puzzle. There are places where they don't tax on each sale. Also, somebody might bring up tips. Hey this is a puzzle lets not get too realistic.

Both you - Thanks for sharing a comment

Terri said...

Can't wait to check back because I'm really want to know where the other money went!

lisleman said...

now that I have posted a new item on the blog and it's been a few days, I'll write the answer. It's NOT a solution to an algebra type problem. Really it's just accounting confusion.

Reference the first puzzle - the 3 guys did pay $9 each for a total of $27 but the store didn't get the whole $27.
If you divide the people into two groups - 3 customers make one group (#1) and let the store and waiter make the other group (#2) you'll be able to account for all the money. Just locate the $30 - group #1 has $3 and group #2 has $27 - this totals $30. No missing money.

lisleman said...

now that I have posted a new item on the blog and it's been a few days, I'll write the answer. It's NOT a solution to an algebra type problem. Really it's just accounting confusion.

Reference the first puzzle - the 3 guys did pay $9 each for a total of $27 but the store didn't get the whole $27.
If you divide the people into two groups - 3 customers make one group (#1) and let the store and waiter make the other group (#2) you'll be able to account for all the money. Just locate the $30 - group #1 has $3 and group #2 has $27 - this totals $30. No missing money.

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