# Thread: Just your Average puzzle.

1. ## Just your Average puzzle.

There are five numbers in a list...
1. <LI>The average of the first two numbers is 9.
<LI>The average of the last two numbers is 17.1
<LI>The average of the middle three numbers is 21.4
<LI>The sum of all five numbers is exactly 4 times the middle number.
<font color=blue> What is the average of the first and last number? </font color=blue>

2. ## Re: Just your Average puzzle.

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2.7</span hide>

3. ## Re: Just your Average puzzle.

<img src=/S/bwaaah.gif border=0 alt=bwaaah width=123 height=15>
You're killing me! You solved it in less time than it took me to construct it. Did you come up with the five numbers? Or, did you find a work-a-round to get to the final solution? I got the idea from another puzzle I was working on, but tried to make it more complex by adding the fifth number. I might have made it simpler rather than more difficult.

Here's the original puzzle if you care to solve:

<hr>There are four numbers. The average of the first two numbers is 8.0, the average of the last two numbers is 7.7 and the average of the middle two numbers is 11.8. What is the average of the first and last numbers.<hr>
<img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

4. ## Re: Just your Average puzzle.

It was just an average answer... <img src=/S/evilgrin.gif border=0 alt=evilgrin width=15 height=15>

It's a simple matter of writing down the conditions as linear equations. For example in the original puzzle: name the numbers a, b, c and d.
<code>
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">a + b = 16.0 (1)
c + d = 15.4 (2)
b + c = 23.6 (3)
</code>
Adding (1) and (2) yields
<code>
a + b + c + d = 31.4 (4)
</code>
Subtracting (3) from (4) yields
<code>
a + d = 7.8
</code>
So the average of a and d is 7.8 / 2 = 3.9</span hide>

5. ## Re: Just your Average puzzle.

I was spending too much time trying to determine exactly what the 4 numbers are and it wasn't even necessary. <img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

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