The answer to last week's math puzzle:

What happened to the thirtieth dollar?

You might remember from back in grade school that
there are five basic axioms in arithmetic:

Addition and multiplication are both commutative.

That is (a + b) = (b + a)
and (a times b) = (b times a)
for all numbers a and b.

Addition and multiplication are both associative.

That is ((a + b) + c = (a + (b + c))
and ((a times b) times c) = (a times (b times c))
for all numbers a, b and c.

Addition and multiplication are distributive.

That is (a times (b + c)) = ((a times b) + (a times c))
for all numbers a, b and c.

These are called "axioms" because they are only assumptions assumed to be 
true and cannot be proven from other math. (We don't REALLY know there 
aren't some numbers a and b somewhere such that (a + b) is NOT equal to (b + 
a) after all there are a lot of numbers out there and we haven't tested all 
of them. We only assume these are true because they just seems so obvious.)

This has nothing to do with the puzzle, I just thought it was interesting.

The twist in the puzzle is at the end.
You don't ADD the two dollars the bellboy kept - you SUBTRACT it.

Original Room Price = $30
The three guys each get a dollar back = ($30 - $3 = $27)
--SUBTRACT-- the $2 the bellboy kept = ($27 - $2 = $25)
The actual price of the room after the rebate = $25 that is ($30 - $5 = $25)

You don't ADD the $2 to $27 to get $29 - you subtract the $2 to get $25

Notice I never say the number $25 so you're not thinking about that as the 
final target.
Also since the bellboy kept $2 your are inclined to think it should be added 
back in at some point.

Missing dollar riddle (dates back to at least the 1930s)
From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Missing_dollar_riddle



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