   What were the five numbers and in what order?

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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? posted Jun 9, 2014

The code is 74658

Solution
let the number be abcde

The fourth number is one more than the second number.ie d = 1+b
The first number is one less than twice the second number. ie a = 2b-1
The second number plus the third number equals ten. ie b+c=10 c=10-b
The fifth number plus the third number equals fourteen ie e+c=14 e=14-c ie e= 14 - (10-b)

The sum of all five numbers is 30. ie a+b+c+d+e = 30
(2b-1) + b + (10-b) + (1+b) + [14-(10-b)] = 30
4b + 14 = 30
4b = 16
b=4

After getting b, we can get all other digits as per the above equations

And the answer is 74658 answer Jun 17, 2014

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