BrainDen.com - Brain Teasers

# Hotel Bill

## 63 posts in this topic

this shows it better:

10+10+10=30=25+2+3 giving the \$3 back gives =>

10+10+10+(-3)=30+(-3)=25+2+3+(-3) or

10+10+10-3=27=25+2

##### Share on other sites

each person actually paid \$9.33 each for the room, so the \$1 is with the desk clerk

##### Share on other sites

I still dont get it. Can someone tell me how its done!

##### Share on other sites

This is a great one. I learned it as a kid 40 years ago. It is simply bad logic. There is no missing dollar. You cannot figure that each person paid \$9.00, they did not. The three of them paid a total of \$25.00 and they then got a dollar each back and the bell hop still has two. Total of \$30.00

##### Share on other sites

It's just how you write the math at the end that makes it so confusing, Each man paid 10 so 10 10 10 then subtract 25 (what the manager kept) and then subract 5 (what the bellboy had) and you equal 30. Sometimes working something backwards makes it easier.

##### Share on other sites

They each paid \$9, only because the bellboy pocketed the other \$2 the remaining \$3 is the amount they got back. They actually each paid \$8.33 and 1/3 cents for the room which was \$25, then the bellboy kept \$2 which brings us to \$27 and they were given back \$3 (\$1 for each person) which makes a grand total of \$30.

##### Share on other sites

basically, each person paid \$9 each, giving the manager \$27. \$2 of these dollars went to the bellboy.

The remaining \$3 come from the \$1 each person got returned to them added together.

A deputy head at my school did the same puzze with pounds, but didn't tell us the answer.

Am I right?

It's not EXACTLY nonsense - pretty cool actually

muahaha messing with innocent minds lol

x

##### Share on other sites
Hotel Bill - Back to the Logic Puzzles

Three people check into a hotel. They pay \$30 to the manager and go to their room. The manager finds out that the room rate is \$25 and gives \$5 to the bellboy to return. 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 remaining dollar?

Hotel Bill - solution

This is a nice nonsense. Each guest paid \$9 because they gave \$30 and they were given back \$3. The manager got \$25 and the difference (\$2) has the bellboy. So it is nonsense to add the \$2 to the \$27, since the bellboy kept the \$2.

This is another famous 'paradox'. I've found it in multiple sites before. And one of them explained it. It said that in these statements, all the information is correct EXCEPT for the last two. "So they paid \$9 each, totalling \$27. The bellboy has \$2, totalling \$29." These are false and misleading statements because in the \$27, it is the \$2 that the bellboy kept that has been accounted for. Which means that there is the \$3 that still needs to be taken in that was given back to the guests of the hotel. And \$27 plus \$3 equals \$30, the same amount that was originally given.

Edited by stilllearning

##### Share on other sites

If they were given back \$3 and that made them actually pay \$9 each then that payment was both to the hotel and the bellboy in turn leaving the \$3 they got back to be the missing \$3.

##### Share on other sites

The three guests paid a total of \$27 out of pocket, of which the bellboy has \$2 and the manager has \$25. There is no missing dollar.

##### Share on other sites

THE PEOPLE ARE GIVEN \$9 EACH THEN FROM THE BELLBOY ANOTHER \$1 EACH WHICH ADDS UP PERFECT

AM I RIGHT OR NOT THINK ABOUT IT

##### Share on other sites

Everthing is fine and there is no loss of \$1. Customers paid \$30, \$10 each of them but manger returned \$5 back. Billboy kept \$2 in between and returned \$3, \$1 to each of them. So now if we calculate they paid \$9 instead of \$10. Total amt paid is \$27 inclusive of the amt which has been kept by billboy. It is like. \$25 Hotel Bill + \$2 Billboy kept + \$3returned = \$30 or other way is \$9 paid by each of them so total is \$27 (inclusive of Hotelbill & \$2 of billboy) and they got \$3 back, \$1 each so {(\$9 * 3)= \$27 = (\$25 + \$2)} + (\$1 * 3) = \$30

##### Share on other sites

There is no extra dollar!

##### Share on other sites
Hotel Bill - Back to the Logic Puzzles

Three people check into a hotel. They pay \$30 to the manager and go to their room. The manager finds out that the room rate is \$25 and gives \$5 to the bellboy to return. 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 remaining dollar?

Hotel Bill - solution

This is a nice nonsense. Each guest paid \$9 because they gave \$30 and they were given back \$3. The manager got \$25 and the difference (\$2) has the bellboy. So it is nonsense to add the \$2 to the \$27, since the bellboy kept the \$2.

where do you get \$27 from, \$25 at the desk, \$3 to the guys, and the \$2 the bellboy kept: 25+3+2=30

##### Share on other sites

I think I can try to clear out the solution.

The problem estates that each person paid \$9 (\$27 total) plus \$2 for the bell hop equals 29. HERE'S THE CATCH (AND THE LIE)!!! The first \$27 already include the \$2 for the bell hop (and \$25 for the rooms), so REAL total cost for all \$3 was in fact \$27. If you add the \$3 returned after the bell hop stole \$2 you get the \$30 originally paid.

Hope this clears any doubts.

##### Share on other sites

YOU"RE ALL WRONG !!!!!!

You don't split the bill into decimals !!!!

The prob exists with how the \$2.00 the bell boy has is begin treated. Each person DID only pay \$9.00 when they got the dollar refund. BUT YOU DO NOT ADD THE bellboys theift of \$2 .00 to the \$27........you SUBTRACT IT....since HE KEPT IT !!!!!!!!!

THEREFORE.............\$27.00 MINUS the \$2.00 for the bellboys sin..........and you get the \$25.00 the room actally costs.

NOTHING COMPLICATED ABT IT. When the directions are given to you.....the joker TELLS you to ADD THE \$2.00, but that is WRONG......you just didn't catch it !!!!!

##### Share on other sites

HERE IS HOW YOU DO THIS SIMPLE ACCOUNTING PROBLEM:

How much all three of you paid from your pocket = how much the hotel manager got + how much the bellboy got .....(i)

How much all three of you paid from your pocket

= you paid 30 chips and got back 3, so you paid 27 chips...........................................................................

............(ii)

How much the hotel manager got

= he got 30 and gave back 5 chips, so he got 25 chips...........................................................................

................(iii)

How much the bellboy got

= the money he took= 2 chips...........................................................................

..................................................(iv)

25+2=27.......so it is not supposed to add up to 30.

##### Share on other sites

I'm not sure,but this is what I wrote...

I think the manager still has it, or the bellboy has it.

##### Share on other sites
Hotel Bill - Back to the Logic Puzzles

Three people check into a hotel. They pay \$30 to the manager and go to their room. The manager finds out that the room rate is \$25 and gives \$5 to the bellboy to return. 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 remaining dollar?

Hotel Bill - solution

This is a nice nonsense. Each guest paid \$9 because they gave \$30 and they were given back \$3. The manager got \$25 and the difference (\$2) has the bellboy. So it is nonsense to add the \$2 to the \$27, since the bellboy kept the \$2.

It's not true that the each paid \$9. As a group, they paid \$27, which is exactly how much money is in possession of the Hotel (\$25) + the bellboy (\$2). So, on average, they paid \$9.67 and 1/3 cent each. They each have 1/3 of the remaining \$3, or \$1.

##### Share on other sites

Both nuttyprofessor and Matthew153 are right. For those of you who are still having trouble understanding the solution and still want to divide the values into non-whole numbers, look at it this way:

Originally \$30 was paid to the manager, \$10 from each person

Then the manager realized that the amount due was really \$25, so he gave back \$5.

Problem was, not all \$5 made it back to the hotel guests. The bellboy stole \$2. That \$2 is the extra that they paid for their room. While it is true that each of them SHOULD have paid \$8.33 (25 divided by 3), they ended up each paying \$9 because the bellboy stole 2 of their dollars, which divided equally (\$2/3) is \$0.67 per guest. \$8.33 + 0.67 = \$9 each. There was no change involved at all, but this is what SHOULD have been. Another way to look at it is, the guests paid \$9 each (=\$27), the bellboy paid -\$2 (negative two...TAKING \$2 is the same as PAYING NEGATIVE \$2) and the manager ended up with the right amount of \$25 (\$27 + (-\$2) = \$25). The only \$30 involved was the original payment but then change was given, and there was never \$29 since the bellboy took instead of paying. If you think about it, it doesn't make sense to say that the manager took 30, gave back 5 (=25), the guests paid 27 (overpaying by 2) and that that overpayment didn't go to the bellboy...

##### Share on other sites

Sure, they each paid \$9, totalling \$27 paid. The Bellboy kept two dollars, and the clerk has the other twenty-five, leaving three dollars with the guests. The wording of the problem counts the bellboy's tip twice (25+2=27, 27+2=29), and doesn't count their change. I think I heard this in Jr. High.

##### Share on other sites

They each paid 9.33 total. The 33 cents each wasn't given back. I would of fired the bellboy for causing all the comotion, because 33 cents is a lot of money when a hotel room is \$9.33.

##### Share on other sites
Actually, I got a totally different answer - and please tell me if I'm wrong:

For the money exchanged: The true bill was \$25 and the bellboy gave each of the three guests a \$1 back. Now, the total exchanged is \$28. And the bellboy has \$2. That equals the \$30.

For the intangible part: You can't figure in that each guest paid exactly \$9 for the room because the room bill was \$25 which can't be divided between 3 people evenly. Each person would have paid exactly \$8.33333333333333 each.

Take the \$8 x's 3 people = \$24

Plus \$3 they were given back = \$3

.33333333333333 x's 3 people = \$1 <--- the missing dollar

and the bellboy has \$2

Total = \$30

- Hope I did this right

You are a dollar short, they paid 9.33 each.

##### Share on other sites
each person didn't pay \$9 because the total bill is \$25. \$2 was subtacted out of the equation unlike everything else was divided and multiplied. you can't multiply and divided and add and subtract in any order you want, do to order of operations. (PEMDAS)Perentases, exponents, multiply, divide, add, subtract. so remember to Please Excuse My Dear Aunt Sally.

WAY TO TRY AND SOUND SMART. IT STATES THAT THEY "PAID" 9 DOLLARS BECAUSE 1 DOLLAR WAS RETURNED. THEY INITIALLY PAID 10 DOLLARS EACH, MINUS THE 1 THE BELL BOY GAVE BACK IS 9. 10-1=9.

30(PAID)-5(RETURNED)=25(BILL)

25(BILL)+3(RETURNED)=28(BILL AND RETURNED)

28(BILL AND RETURNED)+2(BELL BOY)=30 (TOTAL)

##### Share on other sites
YOU"RE ALL WRONG !!!!!!

You don't split the bill into decimals !!!!

The prob exists with how the \$2.00 the bell boy has is begin treated. Each person DID only pay \$9.00 when they got the dollar refund. BUT YOU DO NOT ADD THE bellboys theift of \$2 .00 to the \$27........you SUBTRACT IT....since HE KEPT IT !!!!!!!!!

THEREFORE.............\$27.00 MINUS the \$2.00 for the bellboys sin..........and you get the \$25.00 the room actally costs.

NOTHING COMPLICATED ABT IT. When the directions are given to you.....the joker TELLS you to ADD THE \$2.00, but that is WRONG......you just didn't catch it !!!!!

Dont put so many exclaimations and try to yell at people when your wrong. You are trying to ADD to get to 30 from 25. 25+2(bell boy) is 27. 27+3(returned) is 30. Simple as that. Research before you bash other people. Although, you were correct about the deicmal thing. That is just wrong! haha.