Random Puzzles 

Workings

Hint
Something's wrong with the letter O, and the word 'oifoeront' is important to the answer.

Answer
15 different letters: acdefhilmrstvwy.

Reasoning
The sentences should read:

As you can see, my printer replaces every third letter with the letter 'o'.

How many different letters have been replaced?

Workings

Hint
The first letters of the words are: B, A, S, A, B, B, R, N, B, C.

Answer
BINARY = BRAINY
ABROAD = ABOARD
RASCAL = SCALAR
ALTARS = ASTRAL
BADGER = BARGED
BARKED = BRAKED
MARBLE = RAMBLE
UNABLE = NEBULA
TABLET = BATTLE
CALLER = CELLAR or RECALL

There are some less common anagrams such as:
RASCAL = SACRAL
ALTARS = TARSAL
ALTARS = RATALS
ALTARS = TALARS
BADGER = GARBED
BARKED = DEBARK
MARBLE = BLAMER
MARBLE = AMBLER
MARBLE = LAMBER
UNABLE = UNBALE
TABLET = BATTEL

So you can have an extra half point if you found one of these! There are some even rarer anagrams, but I don't think I'll allow those!

Workings

Hint
A very, very easy puzzle?

Answer
5.

Naturally!

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.