Numbers are things we deal with every day, but sometimes they can be hard to visualize. For instance, how big is a billion (10^9, thousand million, not the traditional English million million)? Billions are good for describing the national debt which in November 2012 in the US was $16,000 billion and was £1,000 billion in the UK. To try and put a billion into context: a billion seconds ago, a 31 year old had not been born; a billion days ago mankind was just about putting in an appearance on earth.
Some more puzzles and paradoxes for you to consider:
Sheet of thin rice paper, one-thousandth of an inch thick. Tear paper in 2, placing one half on top of other. Tear those two in half, placing one half over other. Repeat a total of 50 times (including the times we started out with). How tall is the pile? (2^50 * 1/1000" = almost 17.77 million miles)
Two identical coins (A&B) are placed side-by-side against each other, A is held fixed and B is rolled around A until it is back to its original position. How many complete revolutions of its own center will coin B have made? (2 - when coin B is on the far side of A it with be back in the same orientation it started out having completed one revolution).
2 pounds = 32 ounces
1/2 pound = 8 ounces
Multiplying the 2 and the 1/2 gives 1 pound on one side of the equation, multiplying the 32 and the 8 on the other side results in 1 pound = 256 ounces. Why is this wrong? We didn't multiply the units (2 ft = 24 in, 1/2 ft = 6", 1 SF = 144 sq in).
The following may not use numbers, but they are related to math:
Nobody's perfect; I'm a nobody; therefore I am perfect.
I am a liar.
All rules have exceptions.
[If you know of similar problems/paradoxes, please feel free to bring them up and discuss them]