The Door Code
There are are 4 digits in the code.
The difference between the third digit and the fourth digit is four times the first digit.
The difference between the second digit and the third digit is twice the first digit.
The first digit is twice the fourth digit.
The answer is 2591.
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1 solution
Let the 4 digits be a,b,c and d. From the first statement we know d-c=4a or c-d=4a Similarly for the second statement, c-b=2a or b-c=2a The third statement tells us that a=2d, so by substituting this into both of our first equations, we realise d-c cannot equal 4a since we get 7d=-c (and all the digits must be possible). By substituting a=2d into c-d=4a we arrive at c=9d, since all the digits must be whole numbers (between 0 and 9 inclusive) we know d=1 and c=9. a=2d therefore a=2. We find b=5 from statement 2, giving us 2591