Easy Puzzles 

Workings

Hint
There are no squares of size 5 x 5.

Answer
There are 125 squares without a rook.

Reasoning
61 squares of size 1 x 1
39 squares of size 2 x 2
20 squares of size 3 x 3
 5 squares of size 4 x 4

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
You might need a pen, and some paper.

Answers
EIGHT
TWO
E occurs 148 times, followed by T (137 times), I (91 times), N (90 times), and Y (80 times).
The letters L (ELEVEN, and TWELVE) and D (ONE HUNDRED) both occur twice.
A, B, C, J, K, M, P, Q, Z.
864 letters (excluding hyphens).
SEVENTY-THREE, SEVENTY-SEVEN, SEVENTY-EIGHT.
25 numbers: 2, 3, 10, 12, 13, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
29 numbers: 5, 7, 11, 12, 17, 25, 27, 35, 37, 45, 47, 55, 57, 65, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 87, 95, 97.
Y first appears in TWENTY, and every subsequent number below 100 uses a letter already used.
ONE HUNDRED AND ONE. In US English the AND is usually dropped, so the letter A first appears in ONE THOUSAND.
ONE BILLION.

Workings

Hint
Look at Digit 3 first.

Answer
6394.

Reasoning
Labelling the clues:

Digit 2 is smaller than Digit 4 Digit 4 is two thirds of Digit 1 Digit 1 is two thirds of Digit 3 Digit 3 is three times Digit 2
By (3), Digit 3 is divisible by 3:

   Digit 3 = 3, 6, 9

By (3), Digit 1 is two thirds of Digit 3:

   Digit 1 = 2, 4, 6.

But, by (2), Digit 1 is divisible by 3:

   Digit 1 = 6, and Digit 3 = 9.

By (4), Digit 3 is three times Digit 2:

   Digit 2 = 3.

By (2), Digit 4 is two thirds of Digit 1:

   Digit 4 = 4.