What 5-digit number am I thinking of?

It has two prime digits.
Digit 3 is the highest digit.
Digit 2 is the lowest digit.
Digit 1 is higher than the sum of digits 4 and 5.
Digit 5 is half of digit 4.
Digit 1 is one smaller than digit 3.
Digit 5 is between digit 2 and digit 1

The digit 0 doesn't appear, and there are no duplicates. Don't forget that 1 isn't prime, but 2, 3, 5 and 7 are prime.

Puzzle Copyright © Kevin Stone

workings
hint
answer
print

Share link – www.brainbashers.com/puzzle/zvhe

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

**Note:** BrainBashers has a Dark Mode option – I recommend **not** using your browser's dark mode or extensions for BrainBashers