The Mysterious Code - II
Locked inside a room, you see a Number Pad with this note:
"I am Professor Mad Math. The only way to escape is to punch in the correct Code into the Number Pad. The code is made up of the digits 1 to 9 inclusive, with each digit used exactly once.
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No two consecutive digits are adjacent to each other.
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The digits 2 and 4 are in the second and fourth position in some order.
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The digits 6 and 8 are in the sixth and eighth position in some order.
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The sum of the first five digits is 19.
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The sum of the last five digits is 27.
Can you crack the code?"
The answer is 527418369.
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1 solution
Since this is a nine-digit code, you have to figure a b c d e f g h i . As all of the digit may be used only once and the sum of a + b + c + d + e = 1 9 ; e + f + g + h + i = 2 7 and a + b + c + d + e + f + g + h + i = 4 5 , then e = 1 .
As 2 and 4 must be either in B or D position, the consecutive integer to both of them (3) cannot be in A to D. In similar manner, as 6 and 8 be either in F or H position, 7 cannot be in F to H. Using the sum, we can conclude that a , b , c , d must be in 2 , 4 , 7 , 5 and f , g , h , i be in 3 , 6 , 8 , 9
As 5 is consecutive to 4, 4 cannot be place in B as it will make D = 2 and A and C, either of which has to be 5, be consecutive. Here, we will get d = 4 , b = 2 , a = 5 , c = 7 . In similar manner, 8 cannot be in H as it will make 9 which shall be in G or I consecutive. Using this, we will get f = 8 , h = 6 , i = 9 , g = 3
Thus, the number we are looking for is a b c d e f g h i = 5 2 7 4 1 8 3 6 9