I am white when I am dirty, and black when I am clean. What am I?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

There is a barrel with no lid and some wine in it. 'This barrel of wine is more than half full,' said Curly. 'No it's not,' says Mo. 'It's less than half full.' Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?

The below is a number puzzle. It should be read left to right, top to bottom.
1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
? ? ? ? ? ?
? ? ? ? ? ? ? ?
Question 1: What are the next two rows of numbers?
Question 2: How was this reached?

Which letter of the alphabet has the most water?

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

I left my campsite and hiked south for 3 miles. Then I turned east and hiked for 3 miles. I then turned north and hiked for 3 miles, at which time I came upon a bear inside my tent eating my food! What colour was the bear?

Can you make the number 24 by utilizing the numbers 1, 3, 4 and 6? You must use one number only one time and you can use mathematical operation symbols anytime anywhere.

Can you write down eight eights so that they add up to one thousand?

Christina makes tasty toast in a small pan. After toasting one side of a slice, she turns it over. Each side takes 30 seconds. The pan can only hold two slices.
How can she toast both sides of three slices in 1 & 1/2 instead of 2 minutes?