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?
You can open the excel file with the password being the input of the answer to this question. Enter your name and pass it on.


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1Posted by savage on 2008-03-25 16:11:48
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Do not read further if you wish to work this out for yourself, but I thought I should post the answer and methods used to derive at the answer incase you wish to try and solve similiar puzzles in the future.



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The answer is seven, four, six, five and eight.

This is how I came to the answer using simple algebra:
1. e + c = 14
2. d = b + 1
3. a = 2b - 1
4. b + c = 10
5. a + b + c + d + e = 30

Now we can deduce that if e+c=14 then a+b+d must = 16 since the total of a+b+c+d+e=30.

Next I substitute a & d with their relevant equations:

(2b - 1) + b + (b + 1) = 16
4b = 16
b = 4

Using the what we know from the above result we can solve b + c = 10:

4 + c = 10
c = 6

Next e + c = 14:

e + 6 = 14
e = 8

Next we take a = 2b - 1:

a = 2(4) - 1
a = 7

Finally we can solve d = b + 1:
d = 4 + 1
d = 5

And we have our answer in the order required which is:
a b c d e
7 4 6 5 8

Enjoy

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