Question

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

Answer 1

Answer:  5942

Step-by-step 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