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Sam is a gluttonous kid, so he decides to buy a colorful lollipop at the price of 1$ (one dollar) in the nearest candy store. Though, he realizes that he can't afford it as his budget is just 1¢ (a penny). Anyway, Sam isn't going to give up, so he asks to his friend Tom to change his penny with a dollar.

"Why should I?", asks Tom.

Sam replies: "One dollar is 100 pennies; 100 pennies are 10 pennies x 10 pennies; 10 pennies x 10 pennies are 1/10 of dollar x 1/10 of dollar; 1/10 of dollar x 1/10 of dollar is 1/100 of dollar; I just showed you that one dollar is equivalent to a penny."

How is Sam lying?

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    $\begingroup$ Sam is lying by saying something that he knows to be untrue as if it were true. $\endgroup$ – KSmarts Apr 2 '15 at 21:56
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Sam is simply mixing up the units: dollars, squares of dollar, pennies, squares of pennies. This yields a lot of nonsense.

Sam replies: "100 pennies are 10 pennies x 10 pennies."

This statement is wrong: 10 pennies x 10 pennies equals 100 penny-squared.
(A correct statement would be: 10 times 10 pennies equals 100 pennies.)

"1/10 of dollar x 1/10 of dollar is 1/100 of dollar"

This is also wrong: 1/10 of dollar x 1/10 of dollar equals 1/100 dollar-squared.

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    $\begingroup$ I wonder how much a dollar-squared is worth. $\endgroup$ – Kruga Mar 10 '16 at 10:26
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    $\begingroup$ @Kruga. At today's exchange rate is worth 0.7921 squared euros. $\endgroup$ – Marius Aug 29 '16 at 6:36

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