Question

Four different digits from 1 to 9 are required to open a safe.

1. The sum of the digits is 20.
2. The first digit is greater than the third.
3. The second and fourth digits differ by at least 5.
4. Exactly two digits are squares.
5. The first and fourth digits add up to a prime number.
6. The fourth digit is the lowest.
Can you find the four-digit combination?

Answer 1

Answer: 5942

Explanation:

Clue 4 states exactly two of the digits = 1, 4, or 9

Clue 1 leaves us with the following combinations:

1, 9, 2, 8

1, 9, 3, 7 eliminate by clue 5

4, 9, 2, 5

1, 4, 7, 8

Clue 5 directs us to the following order for 1,9,2,8

2 __ __ 1 --> 2981 or 2891 eliminate by clue 2

9 __ __ 8 --> 9128 or 9218 eliminate by clue 6

9 __ __ 2 --> 9182 or 9812 eliminate by clue 6

Clue 5 directs us to the following order for 4,9,2,5

5 __ __ 2 --> 5492 or 5942 eliminate 5492 by clue 2

9 __ __ 2 --> 9452 or 9542 eliminate by clue 3

Clue 5 directs us to the following order for 1,4,7,8

4 __ __ 1 --> 4781 or 4871 eliminate by clue 2

The only combination not eliminated is 5-9-4-2, which satisfies all six clues.

1) 5 + 9 + 4 + 2 = 20

2) 5 > 4

3) 9 - 2 > 5

4) 4 & 9 but not 1 are included

5) 5 + 2 = 7, which is a prime number

6) 2 < 5, 9, 4