# Where is the missing number?

• Apr 13th 2012, 10:51 AM
benjiman46
Where is the missing number?
Can anyone help me answer this?..

You see a shirt for £97, but you don't have any money.
You buy the shirt, and have £3 change.
£49 + £49 = £98 and your £1 makes £99.

Where is the missing £1?
• Apr 13th 2012, 11:48 AM
FernandoRevilla
Re: Where is the missing number?
Quote:

Originally Posted by benjiman46
Where is the missing £1?

You owe 49 pounds to your dad and 49 to your mum. You have 1 pound so, you need another pound to payng your debt.
• Apr 13th 2012, 11:51 AM
MathoMan
Re: Where is the missing number?
Think of it this way:
Your debt is 100 pounds combined. After giving back 1 pound to your mom and 1 pound to 1 dad reduces your debt by 2. So now your debt is 98 pounds. That means that any number of pounds you have with you can only be used to reduce the debt, and not to increase it. In terms of mathematical operations, the number of pounds you have with you can only be subtracted from the total debt, not added to the debt. The one pound you are left with can only be used to reduce your debt by one, meaning it cannot be added to 98 to get the result 99, but only subtracted from 98 to get the correct answer 97. Get it?

Nothing is missing, you are just forced into paradox by the incorrect operation performed between the debt of 98 pounds and the one pound you have with you.

I hope nothing is lost in translation since English is not my native language.
• Apr 13th 2012, 11:55 AM
MathoMan
Re: Where is the missing number?
Quote:

Originally Posted by FernandoRevilla
You owe 49 pounds to your dad and 49 to your mum. You have 1 pound so, you need another pound to payng your debt.

Oh professor, you should know better than that! ;)
• Apr 13th 2012, 03:44 PM
FernandoRevilla
Re: Where is the missing number?
Quote:

Originally Posted by MathoMan
Oh professor, you should know better than that! ;)

I didn't explain it well. Your correct approach is about the coherence of the shirt's price, and mine one about the coherence of the debt. In your case $49+49-1=97$, in my case $100=1+1+(98-1)+1(\mbox{the pound the son has})$.
• Apr 13th 2012, 03:58 PM
MathoMan
Re: Where is the missing number?
No hard feelings professor, I was just teasing you a bit. Math on!
• Apr 14th 2012, 01:29 AM
FernandoRevilla
Re: Where is the missing number?
Quote:

Originally Posted by MathoMan
No hard feelings professor, I was just teasing you a bit. Math on!

No problem, I am very fond of irony (although provisionally retired, I must confess).
• Apr 14th 2012, 06:11 AM
HallsofIvy
Re: Where is the missing number?
Solution: anyone who pays £97 for a single shirt is obviously crazy. Therefore the "missing £1" is the result of a psychotic episode!
• Apr 14th 2012, 12:20 PM
MathoMan
Re: Where is the missing number?
Quote:

Originally Posted by HallsofIvy
Solution: anyone who pays £97 for a single shirt is obviously crazy. Therefore the "missing £1" is the result of a psychotic episode!

Yep, but that solution is the trivial one. :D