Category: E05: Missing Dollar

The dollar is not missing. The prompt from the first and second paragraph make complete sense, but the third paragraph causes the confusion on if there is a missing dollar. With the change of the $30 the women gave being $5 since they only had to pay $25, is not evenly taken from each women. The most even split that can be made would be if two women had $2 taken from their $10 and $1 taken from the third woman. Now the third paragraph as I said is what causes the confusion of the “missing” dollar. Each woman did in a way pay $9 each at the end, but as mentioned the split isn’t even so it can’t be considered $9 multiplied by 3 is $27 with a missing dollar in the end. Basically, there isn’t a missing dollar since the waiter took the extra dollars from two of the women (when the split is 2:2:1 as I mentioned) and gave $1 back to each women equaling $5 total.

There were 3 ladies, so if the waiter gave each of them one dollar that would equal three dollars. If he has two dollars in his pocket then three plus two equals 5. And if the bill is 25 dollars then there is no extra money. all of the money is accounted for. there is no extra dollar.

There is no missing dollar. Each woman paid $10 for their $30 bill. The actual bill was $25. When the waiter pocketed $2 and returned $1 to each woman, the bill essentially became $27. The $2 in the waiter’s pocket is included in the bill because the women had no idea it was being returned to them. Each woman DID pay $9 each. 9*3=27. The $29 from adding $2 to the bill should not be accounted for, since it was already secretly added to the bill the moment the waiter put it in his pocket.

In the case of the missing dollar paradox there is actually no missing dollar. The prompt starts off with stating that the bill for the meal is $30, which is then evenly split between the three women. The reader then finds out that the actual price of the bill is $25. So the cashier gives the waiter $5 to give back to the three women. The waiter ends up keeping 2 out of the 5 dollars, essentially acting as a tip and then gives each women $1 back. But what is missed is the $25 bill that has technically already been paid. The cashier still has the $30 that the women paid and the cashier only had to give back the $5 that needed to be returned. The prompt then goes on to say that the three women try to split it evenly by all paying $9 which doesn’t make sense since the cashier never gave them their $30 back, only the $5 that needed to be returned. So each woman got $1 back and the waiter received $2 as a tip. There is no missing dollar here.

In the case of the missing dollar paradox there is no missing dollar. The way that the structure is set up is to make the reader think there is a missing dollar but in actuality all the money is accounted for. At the point where the paradox states that the twenty-seven plus two is twenty-nine is correct but your not supposed to be adding the two dollars that the waiter took but the three dollars that was returned to them. The two dollars that the waiter took is already included in the twenty-seven dollars the ladies know to be the bill. By adding the three dollars returned to the women you end with the original thirty.

Essentially, the two dollars that was stolen was a tip. Which ended up with all three women essentially paying $27 for the meal, even though it was a $25 meal.

Since there were 3 women at the table, and only a two dollar “tip” was given, two women paid more than the other one. Which means that one whole number cannot be multiplied by a whole number in order to reach the actual amount of money spent accurately. The bill was $25, each woman in the end paid approximately $8.34 to pay the bill while only two of the ladies “tipped” the waiter one dollar each, and then three dollars was split evenly in between the three diners.

25/3= 8.33333…  (division of equal pay for final bill)

8.34*3=25.02      (equal bill set and paid)

25.02+2=27.02   (equal bill paid + $2 “tip”)

27.02+3=30.02   (Bill and tip + change back)

(The extra two cents appear due to the fact that 8.34 is the rounded figure of 25/3 which is 8.333 (repeating))

From what I concluded there was no dollar missing.  The bill came out to $25.00 so the overall bill including tip would come out to $30.00 total.  The two dollars pocketed by the waiter was his tip.  There was 3 dollars given back to the customer.  In the end the math all adds up.

There is no dollar missing.  The original total bill was $25.00 , but when each of the ladies paid $9.00 each which equals to $27.00.  The waiter had kept the $2.00 which was the tip to make it even when he gives the ladies their change back.  The waiter gave each of the ladies $1.00 back because 27+3=30.

In this paradox there is no missing dollar. The money adds up. A $25 bill, the $2 “tip” kept by the waiter, and the $3 returned the customers. 25+2+3=30.

We are influenced to think that there is a missing dollar because of the extra math that is done at the end of the example, “Three times 9 is $27. The waiter has $2 in his pocket. Two plus 27 is $29.”. This math is unneeded and only included to distract the reader.

There has never been a missing dollar. The situation says that each woman paid $10 for a bill of $30. The cashier then reveals that the actual bill is $25, and gives the waiter five $1 bills to return to the women. The waiter keeps $2 and returns to each woman a $1 bill.

So now the bill is $25. Since each woman was given back $1, they each ended up paying $9, for a total of $27. From this total, the waiter took $2 for himself, bringing the total down to the $25.

Each woman originally paid $10 for a total of $30. They were later given back each $1 in return, bringing the total to $27. With this new total, the women each had to have paid $9. However, the actual bill is still $25, meaning that they have still overpaid. To solve the problem, the waiter takes $2 for himself, causing the total down to the bill’s amount.

“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.” It is the wording of these sentences that confuses readers. With each woman being given back $1, each woman has now paid $9, meaning that the adjusted total is now $27 (something these sentences do not specify). The $2 from the waiter’s pocket is from the $27, and therefore cannot be added to that total. The new adjusted total after the waiter’s removal is $25, which is exactly what the bill needed.

Here is math to illustrate my point one final time:

$10 + $10 + $10 = $30 (original bill)

$25 (real bill)

$30 – $5 = $25          

$5= $1+ $1+ $1+ $1+ $1

Woman 1: $1     Woman 2: $1   Woman 3: $1

$10 – $1= $9

$9 + $9+ $9= $27 (adjusted total)           $30- $1 – $1 –$1 =$27

Waiter: $1 + $1

$27 – $1 – $1 = $25

The restaurant has $25 which is what the real bill required ($25).

Basically, there is no missing dollar.