Brain Teasers
Dollar and Cents
What is wrong with the following logic that "proves" 1 dollar = 1 cent? See if you can determine at which line(s) a mistake is made.
1 dollar
= 100 cents
= 10 cents x 10 cents
= 1/10 dollar x 1/10 dollar
= 1/100 dollar
= 1 cent
1 dollar
= 100 cents
= 10 cents x 10 cents
= 1/10 dollar x 1/10 dollar
= 1/100 dollar
= 1 cent
Hint
Try replacing money (dollar and cent) with length (metre and centimetre).What is 10cm x 10cm?
Answer
The chain of equality breaks down at the second equals sign.10 cents x 10 cents = 100 cents^2 (whatever a square cent is). It's like mixing length (metres) with area (square metres).
It should read 100 cents = 10 x 10 cents.
The same type of error is made again when dollar x dollar is asserted equal to dollar instead of dollar^2.
Here is corrected logic:
1 dollar
= 100 cents
= 10 x 10 cents
= 10 x 1/10 dollar
= 10/10 dollar
= 1 dollar
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Comments
Good one, Marc.
Quirky and odd! Easy for math geeks (yes, units matter!), but it could be quite puzzling for non-science folk.
Nice teaser Marc, as soon as I wrote it out myself, the error was obvious!
I like this one, am going to keep it on file.
I like this one, am going to keep it on file.
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