MHB Unlock the Code - Solve the Challenge!

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A man forgot the code to his work building but remembered five clues that led to the solution. The clues provided relationships between the five numbers, allowing for a mathematical breakdown. By substituting the clues into a sum equation, the values of the numbers were determined. The final solution revealed the code as 74658. The challenge was noted as being particularly difficult yet rewarding to solve.
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Here is another challenge that I thought was fun :cool:

A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were:

The fifth number plus the third number equals fourteen.

The fourth number is one more than the second number.

The first number is one less than twice the second number.

The second number plus the third number equals ten.

The sum of all five numbers is 30.

What were the five numbers and in what order?
 
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Let $A,B,C,D,E$ be the five numbers, in that order. Thus, the clues may be written as:

(1) $$C+E=14$$

(2) $$D=B+1$$

(3) $$A=2B-1$$

(4) $$B+C=10$$

(5) $$A+B+C+D+E=30$$

Substituting (1)-(4) into (5), we find:

$$(2B-1)+B+(B+1)+(14)=30$$

$$4B=16\,\therefore\,B=4\,\therefore\,D=5\, \therefore\,A=7\,\therefore\,C=6\,\therefore\,E=8$$

Hence the code is: $74658$
 
Correct! I thought this was a rather tough puzzle! It took me forever to figure it out!
 
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