# Solve the Mystery of Missing Dollar

### Missing Dollar Riddle

Three friends check into a hotel. They pay \$30 to the manager and go to their room. The manager suddenly remembers that the room rate is \$25 and gives \$5 to the bellboy to return to the people.  On the way to the room the bellboy reasons that \$5 would be difficult to share among three people so he pockets \$2 and gives \$1 to each person. Now each person paid \$10 and got back \$1. So they paid £9 each, totalling \$27. The bellboy has \$2, totalling \$29.

Where is the missing \$1?

The above  missing dollar riddle is a famous problem that illustrates problems of confusion and misdirection in conversation. It illustrates how misdirection and irrelevant facts and questions can foil a person’s clear understanding of a problem. Apply your mind and explain the logic behind the missing dollar.

Follow-up to the above problem – An interesting resolution is often cited as the solution to the above problem. Just read the following paragraph and post a comment whether you agree or not the given resolution to the above mystery.

A few months later, two of the original three guests check into a hotel room in the same hotel. The clerk says the bill is \$20, so each guest pays \$10. Later the clerk realizes the bill should only be \$15. To rectify this, he gives the bellhop \$5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest \$1 and keep \$3 for himself.

Now that each of the guests has been given \$1 back, each has paid \$9, bringing the total paid to \$18. The bellhop has \$3, so \$18 + \$3 = \$21, and the guests originally handed over \$20, so that’s where the missing dollar from the original problem is!

#### Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

## 16 thoughts to “Solve the Mystery of Missing Dollar”

1. miracle says:

on their return — the same

they paid \$18 (\$9 each person). \$15 went to the clerk and \$3 went to the bellhop. so no need to add another \$3 from the bellhop. its already there in the \$18 (\$15+\$3). so to get \$20, you just add the \$2 (\$1 each-the 2 person took back). so no excess there…. 🙂

2. miracle says:

they paid \$27 (\$9 for each person) –\$25 went to the clerk and \$2 to the bell boy. so the \$2 dollars is already included in the \$27 they paid. so the only number your going to add is the \$3 (\$1 each person got back) to get \$30. so nothing is missing.

3. Room rent=25, so each has paid \$8.33
Among remaining \$5 , bellboy had kept \$2 and return \$1 to each one.
so each one had pay \$9.33 not \$9.Which totals \$ 30(28+2)

4. Anish says:

On the one hand, the question is about the savings and on the other hand, comparison is being done with the amount paid. If we compare same things, there would not be any difference.

5. Xpenditure+balance in hand = total amount. 27(9*3) + 3(1+1+1)=30 xpenditure=roomrent+bellboycharge. 27=25 + 2

6. Daemion says:

They paid \$9 each totaling \$27 of which the manager has \$25 and the bellboy \$2.

7. NANDEESH says:

I think this puzzle is one of the most glorified puzzles but a stupid one.

8. Avijit says:

As You Know Room Rent Is \$30. So three Friend’s are paid \$10 each.And exact cost of room is \$25.Manager send rest of money to the hand of Bell boy \$5.but he take \$2 for easy to distribute them.so they return \$1 each now problem is that if they paid \$9 each then total money is \$9*3=\$27.
And bell boy take \$2 so total amount =\$27+\$2=\$29.
Missing \$1. ok.
suppose they paid \$8*3=\$24.
So remainder is =\$6.
We add \$1 in side of room rent=\$24+\$1=\$25.
now remainder = \$5
bell boy take \$2.
so now remainder =\$3
They equally distribute=\$1 each.

Now Problem Is solve
They Paid=\$9 each.
\$2 have in bell boy pocket.
\$1 problem is also solved.

9. Vijayendra Bose says:

Simple explanation:- Since \$1 has been returned to each of the three friends, the total paid by them is no longer \$30. The total paid by them is now \$27. So the room rate of \$25 and the money pocketed by the bell boy i.e \$2, also add up the the same total of \$27.
The problem statement tries to confuse us into comparing with the original total of \$30 instead of the new total of \$27

10. GVS says:

Expenditure by some person(s) = Income of some other person(s)

3 people expended \$27 = \$25 income of hotelier + \$2 income of bellboy

\${[3*(10-1)]} = \$25 + \$2

\$3*9 = \$27

\$27 = \$27.

11. GVS says:

Expenditure made by some person(s) = Income of some other person(s)

Here the 3 people has expended \$25 income of hotelier + \$2 income of
{[3*(10-1)] = 27} dollars = bellboy

Therefore, \$27 = \$27.

Thats it.

12. Ajay says:

well its simple and nothing complex that appears in it..

they paid \$25+\$5. out of which \$3 were given back to them amounting to \$28 and \$2 lies with the waiter which totals to \$30.

Its the language which is actually confusing here, but the calculation part is pretty simple and all this confusion only appears because neither \$25 not \$5 and also not \$2 happens to be the multiple of 3.

13. 2\$ should be not be added at the end of statement rather these 2\$’s should be subtracted..to get 25\$

14. priyank says:

in 1st case out of 25\$ eash paid 8\$ and remainind 1\$ is 0.33\$=25\$.they received 1\$ back therefore 25\$+3\$=28\$ and bellboy keep the 2\$. there fore 25\$+3\$+2\$=30\$.
in 2nd case out of 15\$ each share 7.5\$=15\$. they get back 1\$=2\$ and bellshop keep 3\$. therefore 15\$+2\$+3\$=20\$.

15. Combining Daemion’s and Anish’s we get the complete answer. Kudos guys 🙂