Bad mathematician

[Emporion]

Math!!! It Isn't So Straightforward
Ok, here goes...
Math seems pretty straightforward. And it's either simple calculations or complex ones. But there is always a solution...Or is there!!!

Let's try this. (figures are just examples and are not reflective of any rates. *grin*)

3 guys who were traveling stopped at a motel for the night. They got a not-so-expensive room for themselves, which cost them $30. So each guy had to shell out $10. This seemed to be a good deal for a stay there.

Just before checking out in the morning, room service came by and told them that the manager had given them a $5 discount. He returned the same to them. The 3 guys each took $1 back and tipped the room service guy with the remaining $2. And off they went headed back home.

Now let's go back and calculate the equation!!!
Each guy 1st spent $10, but took back $1 later. So in the end each spent $9. So 3x9=27. And the room service guy was tipped $2. So 27+2=29.
Hmmmm!!! $29 has been accounted for. So where is that remaining 1 dollar???

Math!!! Simple, but sometimes, complicated, or shall we say, Mind Boggling!!!

By Clifford AGA

I wrote:

David The arithmetic is totally right, but the logic is off. You're missing something.

This is another approach which is more LOGICALLY sound.

10x3=30
(10x3)-5=30-5 add in $5 discount
((9+1)x3)-2=(27+3)-2 each guy gets $1 back and the tip is $2
30=30 simplify

Don't forget, numbers don't lie. People lie. 4/20/2011

Does anybody know what the flaw in this guy's logic is? I know it's wrong, but I can't see where it's wrong.

[Eleazar]

Now let's go back and calculate the equation!!!
Each guy 1st spent $10, but took back $1 later. So in the end each spent $9. So 3x9=27. And the room service guy was tipped $2. So 27+2=29.
Hmmmm!!! $29 has been accounted for. So where is that remaining 1 dollar???

Nice problem, Emporion. The mistake here is...

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...that the $2 tip is included in the $27 dollars the three guys spent. Overall they spent $27: $2 tip, and $25 to the hotel. The remaining $3 they kept for themselves ($1 each), totalling $30.

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[Emporion]

Now let's go back and calculate the equation!!!
Each guy 1st spent $10, but took back $1 later. So in the end each spent $9. So 3x9=27. And the room service guy was tipped $2. So 27+2=29.
Hmmmm!!! $29 has been accounted for. So where is that remaining 1 dollar???

Nice problem, Emporion. The mistake here is...

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...that the $2 tip is included in the $27 dollars the three guys spent. Overall they spent $27: $2 tip, and $25 to the hotel. The remaining $3 they kept for themselves ($1 each), totalling $30.

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Ah, now I get it. Thank you.

[Chido-Wan Kenobi]

3 guys who were traveling stopped at a motel for the night.
Each guy 1st spent $10, but took back $1 later. So in the end each spent $9. So 3x9=27. And the room service guy was tipped $2. So 27+2=29.
Hmmmm!!! $29 has been accounted for. So where is that remaining 1 dollar???

Math!!! Simple, but sometimes, complicated, or shall we say, Mind Boggling!!!

By Clifford AGA
I know it's wrong, but I can't see where it's wrong.

Yeah, this is an old one indeed, back from the days when Alexander wasn't "the Great", but just "the Pretty Good".

The trap you are falling into is assuming that the actual amounts paid by the "guys", plus the money stolen by the "room service guy" must equal 30. No, the only real money in the story is [$ the guys GOT BACK, which is $3], [$ in the concierge's pocket, which is $2] and [$ in the Hotel manager's hands, which is $25]. You will agree that the sum of these three amounts is $3 + $2 + $25 = $30, the original "real money". All the rest is just a play of words.

It will become clearer to you if you change the numbers a bit. For instance, say the room was actually worth $10/night, not $25. So, the manager would return $20 via the concierge, who, using the same logic as previously, might decide to pocket $8, and return $4 to each of the guests. Now you will see that, since in fact they paid only $6 each, 3 x $6 = $18, plus the $8 the concierge stole, gives you a total of $26. And now, you appear to be missing $4.

Worse, even. Say the room is actually $40/night. Now the concierge could go back to the guests, and demand an extra $6 from each - planning to bring $10 to the Manager and keep $8. Now, since they effectively paid $16 each, 3 x $16 = $48 + $8 in the concierge's pocket = a total of $56 ! The room was only $40 !! So you've CREATED $16 out of thin air !!! (Good business plan, I should say.)

So there...