Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

The answer I give is yes, but what I mean is no. What was the question?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Aaron, Brad, Christopher, Danny and Elvis decided to play a game of tiddlywinks. In this game they decided that one win will get 1 point for winning, 0 for losing and 1/2 in case of a tie.

They finished the game in alphabetical order and it was found that the scores were different for each person.

Based on the following two statements, can you find out the result of the individual games?
Brad: No one could finish like me, without a loss.
Elvis: No one played worse than me, I finished without a single win.

Can you circle exactly four of these numbers such that the total is twelve?

1 6 1
6 1 6
1 6 1
6 1 6

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

Let's play a word game. Following are some meaningless words that can be completed by adding random letters on either side of the word.

For example, the word "rdo" can be formed into "pardon".

Using the same technique, can you complete the given words?
ecalc
airb
rinci
tibac
uidel
gorit
igna
eyho

What can you catch but never throw?