## Saturday, December 16, 2017

### Three Water Bottles

You have three water bottles with capacities of 8 quarts, 5 quarts, and 3 quarts. The largest bottle is filled with water, and the other two are empty. If there are no graduation marks on any of the bottles, how can you split the water evenly so that two of the bottles contain exactly 4 quarts each? You can only use these three bottles. Click below for the answer.

## Saturday, December 9, 2017

### The Compulsive Gambler

You are approached by a compulsive gambler with the following proposal. You are to flip a fair coin four times. If heads and tails both appear twice each, he will pay you $11. If any other combination of heads and tails appears, you have to pay him only$10. Do you take the wager? Click below for the answer.

## Saturday, December 2, 2017

A lily pad starts out very small, but doubles in size every day. After 60 days it has completely covered a pond. After how many days had it covered one-quarter the area of the pond? Click below for the answer.

## Saturday, November 25, 2017

### Three Coin Flips

The following game has a $10 entry fee. You are to flip a fair coin three times. The first time it comes up heads you are paid$5. The second time it comes up heads you're paid an additional $7. The third time it comes up heads you're paid$9 more, for a possible maximum prize of $21. Would you pay the$10 entry fee to play?

If not, what would be a fair price for this game? Click below for the answer.

## Saturday, November 18, 2017

### One equals 0.999...

The following is a mathematical proof that 1 is equal to 0.999.... What's wrong with it? Click below for the answer.
$x = 0.999...$
$10x = 9.999...$
$10x = 9 + 0.999...$
$10x = 9 + x$
$9x = 9$
$x = 1$

## Saturday, November 11, 2017

### Two equals one?

The following is a mathematical proof that two equals one. What's wrong with it? Click below for the answer.
$a = b$
$aa = ab$
$aa - bb = ab - bb$
$(a + b)(a - b) = b(a - b)$
$a + b = b$
$a + a = a$
$2a = a$
$2 = 1$

## Saturday, November 4, 2017

### State Names

There's only one letter in the English alphabet that is not used in the name of any of the 50 United States. Do you know which letter it is? Click below for the answer.