Brain Teasers and Puzzles

A box for your workings out:

Hint: What can digits 4 and 5 be?

Answer: 71842.

The number can be represented as:

_ _ _ _ _

Since digit 5 is half of digit 4 we have four possibilities:

_ _ _ 2 1
_ _ _ 4 2
_ _ _ 6 3
_ _ _ 8 4

But since digit 1 is higher than the sum of digit 4 and digit 5 we can eliminate two possibilities leaving:

_ _ _ 2 1
_ _ _ 4 2

Since digit 5 is between digit 2 and digit 1, we can eliminate _ _ _ 2 1, leaving:

_ _ _ 4 2

Since digit 1 must be higher than the sum of digit 4 and digit 5 we have three possibilities:

7 _ _ 4 2
8 _ _ 4 2
9 _ _ 4 2

But digit 1 is 1 smaller than digit 3 we can eliminate 9 _ _ 4 2, leaving

7 _ 8 4 2
8 _ 9 4 2

Since digit 2 is the lowest number, it must be 1:

7 1 8 4 2
8 1 9 4 2

The answer has exactly 2 prime digits, which only leaves

7 1 8 4 2.