Where is the missing $1?

Where is the missing $1?

Postby Guest » Thu Feb 04, 2016 3:00 am

missing.jpg
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Guest
 

Re: Where is the missing $1?

Postby Guest » Thu Feb 04, 2016 5:38 am

This is a very old problem, one which I'm sure has lots of explanations on the internet.

Consider:
Amount paid by Mom + Amount paid by Dad + Amount paid by you = Cost of shirt
Which is the same as:
49+49+(-1) = 97
(You paid \$-1 because you gave yourself money from the change)
This makes sense.

The calculation at the bottom is
Amount paid by Mom + Amount paid by Dad - Amount paid by you
Which doesn't correspond to anything, and doesn't make sense (why should this be 100?).

Another way of looking at it is:
Amount Initially paid by Mom + Amount Initially paid by Dad = Cost of shirt + Change given to Mom + Change given to Dad + Change given to you
50+50 = 97+1+1+1
Rearranging gives
Total paid by Mom + Total paid by Dad = Cost of Shirt + Change given to you
49+49=97+1
In terms of physical money, 97 is in the shop, 1 is with you, which corresponds to the 49 taken out of each of the wallets of Mom and Dad.

The incorrect sign assigned to the \$1 is the cause of the incorrect calculation and the "missing \$1".

Hope this helped,

R. Baber.
Guest
 

Re: Where is the missing $1?

Postby leesajohnson » Wed Mar 09, 2016 5:47 am

It's just a tricky question
The cost of shirt is \$97
So you have paid \$97 for the shirt and divided \$3 into three parts \$1 you have and other \$2 you have given to the mom and dad so it's total is \$100.

leesajohnson
 

Re: Where is the missing $1?

Postby Guest » Wed Mar 09, 2016 10:25 am

You are all missing the fact that You borrowed \$50 from each of Your Mom and Dad and You have only paid back \$1 to each. You have still \$49 to payback to each. So that is \$98 still to payback and You have got \$1 in Your pocket. There is also the \$2 You paid back earlier, so breaking it into 3 bits that makes 98 + 1 + 2 = 101 .... where did the extra \$1 come from?.
Guest
 

Re: Where is the missing $1?

Postby Guest » Fri Mar 11, 2016 10:47 pm

You can't just add figures from the question arbitrarily and expect it to add to 100. It makes no sense.
For example: Amount Paid by Parents+Amount owed to Parents = 98+98 = 196, where did the extra 96 come from?
Your sum is:
[Liability] Amount still owed to Parents
+ [Asset] Amount still owned by you
+ [Transfer] amount previously paid to parents (which is already accounted for)
Why would you think this should be 100? Adding your liabilities to your assets is nonsensical.

I think the wiki page explains it pretty clearly:
https://en.wikipedia.org/wiki/Missing_dollar_riddle

Hope this helped,

R. Baber.
Guest
 

Re: Where is the missing $1?

Postby Guest » Fri Mar 11, 2016 10:53 pm

Apologies, in my last post, I meant to say that adding assets, liabilities, and transfers is nonsensical (adding assets to liabilities does makes sense).

R. Baber
Guest
 


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