Random Puzzles 

Workings

Hint
The answer is right in front of you.

Answer
Mississippi.

The diagram is actually the word 'mississippi' on its side.

Workings

Hint
Who is in last place?

Answer
This cannot happen, you cannot overtake the person who is in last place, as there is no-one behind them!

Ovetaking = passing someone who is ahead on the same lap, this is a change of position, e.g. 4^th moves up to 3^rd.

Lapping = passing someone who is a full lap behind, this isn't a change of position, e.g. 4^th stays 4^th.

Workings

Hint
How many 2 x 2 squares are there?

Answer
There are 128 squares without a rook.

Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are  6 squares of size 4 x 4.
There is   1 square  of size 5 x 5.

Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.

Workings

Hint
It might be easier to find the S first.

Answer
Start with the P in the 5^th row, 6^th column: