Random Puzzles 

Workings

Hint
How many 2x2 squares are there?

Answer
There are 93 squares without a rook.

Reasoning
There are 60 squares of size 1x1.
There are 33 squares of size 2x2.

Giving a total of 60 + 33 = 93 squares.

Workings

Hint
This is nothing to do with pets.

Answer
Goldfish.

All of the others are mammals. If you suggested Cow I will let you have half a mark!

Workings

Hint
There are many answers, however, Z doesn't appear very often.

Answers
Choose from: luxury, struts, stylus, syrupy, trusts, twisty.

Other less common words include: scuzzy, syrups, syzygy, trouty, trusty, tryout, trysts.

Workings

Hint
Start with the possible answers where the first digit is a prime number, and then look at the third digit.

Answer
23,475.

Reasoning
By (1), the first digit is prime:
   2----
   3----
   5----
   7----

By (3), the third digit is twice the first digit, so we can eliminate 5---- and 7----:
   2-4--
   3-6--

By (4), the fourth digit is the third digit plus three:
   2-47-
   3-69-

By (5) the fifth digit is the difference between the first digit and the fourth digit:
   2-475
   3-696

We know from the introduction that no digit is repeated, so we can eliminate 3-696. And, by (2) the second digit is the fifth digit minus the first digit:
   23475