Easy Puzzles 

Workings

Hint
The number is less than 20.

Answer
8.

Reasoning
We need a number (N) such that:

2 x N = 14 + N
             —
             4

Multiply throughout by 4 to give:

8 x N = 56 + N

So:

7 x N = 56

So N = 8.

Double-Checking
Its double is 16.

Its quarter is 2.

So its double is fourteen more than its quarter.

Workings

Hint
There are no squares of size 5x5.

Answer
There are 125 squares without a rook.

Reasoning
There are 61 squares of size 1x1.
There are 39 squares of size 2x2.
There are 20 squares of size 3x3.
There are  5 squares of size 4x4.

Giving a total of 61 + 39 + 20 + 5 = 125 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:

Workings

Hint
Look at the first few characters of each word.

Answer
augment.

The first three letters are the same as the first three letters of the months in order.