Puzzle ZVHE 

Workings

Hint
What can digits 4 and 5 be?

Answer
71842.

Reasoning
The number can be represented as:

   - - - - -

By (5), Digit 5 is half of Digit 4, so we have four possibilities:

   - - - 2 1
   - - - 4 2
   - - - 6 3
   - - - 8 4

By (4), Digit 1 is higher than the sum of Digit 4 and Digit 5, so we can eliminate two possibilities, leaving:

   - - - 2 1
   - - - 4 2

By (7), Digit 5 is between Digit 2 and Digit 1, so we can eliminate - - - 2 1, leaving:

   - - - 4 2

By (4), Digit 1 must be higher than the sum of Digit 4 and Digit 5, so we have three possibilities:

   7 - - 4 2
   8 - - 4 2
   9 - - 4 2

By (6), Digit 1 is 1 smaller than Digit 3 we can eliminate 9 - - 4 2, and fill in Digit 3, leaving:

   7 - 8 4 2
   8 - 9 4 2

By (3), Digit 2 is the lowest digit, and must be 1:

   7 1 8 4 2
   8 1 9 4 2

By (1), the only possibility is:

   7 1 8 4 2