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
There are no duplicates and the digit 0 doesn't appear.
Don't forget that 1 isn't prime.
Puzzle Copyright © Kevin Stone
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Hint
What can digits 4 and 5 be?
Answer
71842.
Reasoning
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.
