The Missing Dollar Paradox
Three ladies go to a restaurant for a meal. They receive a bill for $30. They each put $10 on the table, which the waiter collects and takes to the till. The cashier informs the waiter that the bill should only have been for $25 and returns $5 to the waiter in single dollar bills. On the way back to the table the waiter realizes that he cannot divide the bills equally among the ladies.
Since they don’t know the total of the revised bill, he decides to put $2 in his own pocket and give each of the ladies $1.
Now, each of the ladies paid $9. Three times 9 is $27. The waiter has $2 in his pocket. Two plus 27 is $29. The ladies originally handed over $30.
Where is the missing dollar?
- As a Reply to this page, write a brief and clear explanation for the “missing dollar.”
- Feel free to consult with your classmates.
- Complete your work by the end of class today.
Before the waiter gave the ladies 1 dollar each, they were paying 8 dollars each. 3X8=24. Then add the 1 dollar for each makes 27. 24+3 =27. Then, there is the two dollars that the waiter held in the pocket. 27+2=29. There is clearly a missing dollar.
I think that since the money can’t be divided back equally, I think the waiter kept the extra dollar. Each of the ladies paid 24 before they were each given one more dollar. The waiter kept 2 in his pocket, or so he thought. It would have to be the waiter that has the extra dollar since he was the one dividing up the money back to the ladies in the first place.
There is no missing dollar because the women spent $27, of which $25 went on the bill and $2 went to the waiter. The $2 that went to the waiter came from the $27 spent, with the other $25 going on the bill. There is $25 in the cash register, $2 in the waiter’s pocket, and each of the three women has $1.
if they all placed 10 dollars on the table and the bill ended up being 25 and the waiter pockets 2 dollars that is 25+3+2= 30 there is no missing dollar. That would not mean that the bill was now 27 dollars and each and the laddies pay 9 because they they technically paid 9 dollars and something cents because of those two dollars in waiters pocket, however the ladies do not know the waiter pocketed to dollars so for they that is what happened.
If the bill is $25 and they overpay by $2, then the two dollars in the waiters pocket would be the extra amount. You’d subtract 2 from 27, not add. The original price is not relevant here.
*I did just rephrase this whole paradox…but I think I’m on to something here by doing so.*
The ladies paid 30 dollars for their meal, and they split it three ways. (30 ÷ 3 = 10)
The waiter brings the 30 dollars to the till and was told that the bill is actually 25 dollars. Therefore, he received 5 dollars back. (30-25=5) The waiter then realizes that he cannot (and no one can) split 5 dollars equally three ways. (5 ÷ 3 = 1.66….) The waiter decides to keep 2 dollars to himself and distributes the remaining three dollars to each person.
Now, each lady really paid 9 dollars (9 × 3 = 27), there are two extra dollars in the waiter’s pocket (27 + 2 = 29). This does not add up to 30.
However, instead of adding the two dollars, maybe you can take away the two dollars the waiter kept for himself. The two dollars the waiter kept…well it’s really no longer a part of the women’s money. It is now the waiter’s money.
So if the women paid 27 dollars for their meal, and the meal’s price was 25 dollars, (27 – 2 = 25). Maybe the waiter was being nice and gave the women a discount off their meal? The 25 dollars the women paid matched to the total of 25 dollars of the actual bill (with the two dollars the waiter kept from the initial payment of 30 dollars of the meal).
I think that the waiter has the missing dollar, because if the cashier gave back 5 dollars meaning that the bill was 25 it wouldn’t have been split equally between the three customers. Each customer would have to pay $8.33. But he gave them each back 9 dollars making there only two dollar left which he took.
The throw off here is the fact that they try to convince us the bill was $27 which it was not. It was $25. Therefore,$25 went into the cash register, the waiter stashed $2, and each lady was given a dollar back which adds up to $30.
The bill was $25 – “the bill should only have been for $25”
The three ladies received a dollar each – “give each of the ladies $1.”
The waiter kept $2 and kept it in his back “He decides to put $2 in his own pocket”
25+3+2 =30 There is no missing dollar
The women receive $5.00 back, but you cannot split $5.00 among three people evenly, so when you divide $5.00 by three people you get $1.6666, so the waiter gave each woman $1.00 back and kept the $0.6666 cents from each of the women, which rounds to $2.00. Therefore, there is no missing dollar.
There is no missing dollar since the women handed the waiter $30 and the cost of the meal is $25 dollars. The change is $5. (30 – 25 = 5) The waiter hands each lady (total of 3 ladies) $1 each so receiving $3 dollars back total. The waiter keep the last two dollars for himself. ($3+ $2 =$5). The ladies DID have to paid 9$ each, with total meal costing $27 however the two extra dollars included in their bill is the two dollars that the waiter kept for himself, the last $3 was return to the women. There’s no missing dollar.
There are very good reasons here, mostly the observations that the original bill is irrelevant, and the $2 in the waiter’s pocket is the difference between $25 and $27.
The easiest way to “reframe the question” to eliminate the confusion is to imagine this slightly different scenario.
1. The waiter begins by presenting the correct bill: $25.
2. The ladies each pay $10, expecting $5 change to split or leave as a tip.
3. The cashier gives the waiter 5 one-dollar bills.
4. The waiter gives the ladies just 3 one-dollar bills, pocketing two.
5. The ladies notice the theft immediately and have the waiter fired.