Random Puzzles 

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.

Workings

Hint
How many letters does each name have?

Answer
Simon married Teresa: their names have 11 letters when combined.

Workings

Hint
What can digit 4 be?

Answer
6849.

Reasoning
Digit 4 must be a multiple of 3:
   ---3
   ---6
   ---9

Digit 3 is one more than Digit 9 ÷ 3:
   --23
   --36
   --49

Digit 2 is twice Digit 3:
   -423
   -636
   -849

But Digit 4 is one more than Digit 2, which only leaves:
   -849

And Digit 1 is three smaller than Digit 4:
   6849.

Workings

Hint
Try writing the numbers out as letters.

Answer
45.

Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1  + length("ONE")       = 4
4  + length("FOUR")      = 8
8  + length("EIGHT")     = 13
13 + length("THIRTEEN")  = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY")    = 36
36 + length("THIRTYSIX") = 45