Four different digits, 1–9 are required to open a safe. The first and third numbers total ten; the second number is no more than four; the third number is a prime number; the fourth number is three less than the first; and the second number is one less than the fourth.
Can you find the four-digit safe combination?
Difficulty rating:
Easy. 3/10
Solution:
Firstly, we note that the first and the third digits total 10. And the third digit is a prime number. So, the possibilities are:
First digit Third digit
3. 7
7. 3
8. 2
It is also given that the fourth number is three less than the first. This means that the first digit cannot be 3 because that would make the fourth digit as 0.
Therefore, the first digit is either
a) 7 and the third digit is 3. This would make the fourth digit as 4 and the second digit as 3. But, in this case, the second and the third digits are the same. So, this can't be the case.
or
b) 8 and the third digit is 2. This would make the fourth digit as 5 and the second digit as 4. This is the only solution that satisfies all the conditions. Therefore, the four digit safe combination is 8425.