# Math flaws could be very subtle.

#### chesart1

Joined Jan 23, 2006
269
The difficulty in math is that a faulty solution to a problem could look perfectly logical.

Take the following example.

Three man enter a hotel and ask the clerk for three rooms. They each pay the clerk ten dollars. The clerk gives the money to the manager who saids, "here is five dollars. I want you to give one dollar back to each person and keep two for yourself."

Now for the faulty logic. The clerk gave one dollar back to each person. That means each person paid nine dollars. 9 dollars per person x 3 people equals 27 dollars. Twenty seven dollars plus the two dollars the clerk kept equals 29 dollars. Where did the other dollar go?

#### Dave

Joined Nov 17, 2003
6,970
The difficulty in math is that a faulty solution to a problem could look perfectly logical.

Take the following example.

Three man enter a hotel and ask the clerk for three rooms. They each pay the clerk ten dollars. The clerk gives the money to the manager who saids, "here is five dollars. I want you to give one dollar back to each person and keep two for yourself."

Now for the faulty logic. The clerk gave one dollar back to each person. That means each person paid nine dollars. 9 dollars per person x 3 people equals 27 dollars. Twenty seven dollars plus the two dollars the clerk kept equals 29 dollars. Where did the other dollar go?
Its a good con trick, and we 'bubbled' it in the thread thingmaker3 linked to. The trick is in the way you say it - it should be $27 +$3 (which was returned) to give you your $30; or conversely you could say its$27 - $2 (taken by the manager) to give you your$25.

Given that 33% of British people think that Mount Everest is in Europe, I am not surprised this one is easily confusing to people!

Dave

#### recca02

Joined Apr 2, 2007
1,214

#### thingmaker3

Joined May 16, 2005
5,084

#### kautilya

Joined Apr 26, 2007
39
There is no flaw or subtlety in this problem. When the manager returned $5, they effectively paid only 25$! That is, 25/3 = 8.125$apiece. the remaining 5$ was returned by the clerk in which he kept $2 for himself. #### recca02 Joined Apr 2, 2007 1,214 There is no flaw or subtlety in this problem. When the manager returned$5, they effectively paid only 25$! That is, 25/3 = 8.125$ apiece. the remaining 5$was returned by the clerk in which he kept$2 for himself.
it's obvious if put that way,
but the question needs u to find the solution from the questioner's perspective which in this case is wrong to begin with hence it becomes confusing and that is where the subtlety comes from.
this one is quite fun to bamboozle ppl with.

#### Dave

Joined Nov 17, 2003
6,970
this one is quite fun to bamboozle ppl with.
What's amazing about it is that you can explain it to someone and they still don't get it! That to me, is the true mark of how good this conundrum is.

Dave

#### Ryno3030

Joined Dec 1, 2007
9
It seems to me that the problem lies with the faulty logic of people, not any difficulty with math.

#### Dave

Joined Nov 17, 2003
6,970
It seems to me that the problem lies with the faulty logic of people, not any difficulty with math.
Indeed. The maths is perfectly plausible, however people fail to see this because of the way it is told. It is the same failing in people that scam artists exploit.

In the UK, we have a TV programme called The Real Hustle which shows this being exploited every episode.

Dave

#### Mark44

Joined Nov 26, 2007
628
I wouldn't even dignify this as a math (or maths) problem, which implies the possibility of requiriing something more involved than ordinary arithmetic. It's an interesting problem nonetheless.

#### aliashar86

Joined Nov 23, 2006
71
nothing to get worried.

9 * 3 = 27 ok and hey u forgot 2 dollars also given to the clerk so left with 25 which is the same amount as if we subtract 30 -5=25.