Random Puzzles 

Workings

Hint
Where was Dave standing when he fell?

Answer
Dave fell off the very bottom rung of the ladder!

Workings

Hint
Look at every third letter.

Answer
The BrainBashers electronic word processor has been playing up.

It is replacing every third letter with an a. What should this paragraph read?

Workings

Hint
The sequence is related to 1, 2, 3, 4.

Answer
20.

Each term's initial letter position in the alphabet:

1 = One = O = 15^th letter.
.
.
4 = Four = F = 6^th letter.
.
.
.
20 = Ten = T = 20^th letter.

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.