Random Puzzles 

Workings

Hint
How many miles did I travel?

Answer
I had lost 4 gallons.

Reasoning
I travelled at 50mph for 4 hours, which is 200 miles.

I used 25 gallons every 25 miles, so I used 8 gallons travelling those 200 miles.

I started with 12 gallons and used 8 gallons, so I lost the other 4 gallons.

Workings

Hint
Since Dale had a second place, what does this tell us about Chris?

Answer
Race 1: Billie, Chris, Alex, Dale.
Race 2: Chris, Dale, Alex, Billie.

Reasoning
Since Chris always beat Dale, and Dale had a second place, one race must have been Chris first and Dale second.

Billie therefore won the other race, with Chris second.

Since only one runner finished in the same place in both races, this must have been Alex in third.

Workings

Hint
The sequence is related to prime numbers.

Answer
29.

Each term increases by the next prime number.

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.