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For context: I am not old enough to be receiving the AARP magazine, however both my parents receive it and I enjoy reading the AARP magazines.

I have recently been reading the most recent AARP magazine, and decided to check out the BrainGames (which is basically a puzzle page).

I am currently stuck on the puzzle "Sum Things To Consider".

The main idea of this puzzle is that there is a certain rule behind how the final result is computed.

For example: (Credit: Me)

$$\begin{align}\boxed1+\boxed2+\boxed3=&\,\boxed{52}\\\boxed4+\boxed5+\boxed6=&\,\boxed{65}\\\boxed7+\boxed8+\boxed9=&\;\boxed?\end{align}$$

Which has the answer

167

because

We first write out the sum 7+8+9=24 -> twentyfour.

Then, converting Text->A1Z26, we get 20 23 5 14 20 25 6 15 21 18.

Finally, add it all together to get 20+23+5+14+20+25+6+15+21+18=167

For the other 2 sums, 1+2+3=6 -> six -> 19 9 24 -> 19+9+24=52
and 4+5+6=15 -> fifteen -> 6 9 6 20 5 5 14 -> 6+9+6+20+5+5+14=65

however I am not sure how to solve this edition's version of "Sum Things To Consider":$$\begin{align}\boxed1+\boxed2+\boxed3=&\,\boxed{\text{X}}\\\boxed4+\boxed5+\boxed6=&\,\boxed{\text{N}}\\\boxed7+\boxed8+\boxed9=&\,\boxed{\text{?}}\end{align}$$Here's my attempt at solving this:

I think

7+8+9=D

because

Convert the letter results to A1Z26. Then we have that 6->X=24 and 15->N=14. And we have 7+8+9=24.
We have that 24-15=9, 15-6=9, and that X-N=24-14=10.

So, we see that the letters, when converted to A1Z26,

have a numerical difference of 9+1=10 (the 9 being the difference between the sums) and therefore
7+8+9=24->N-10=14-10=4=D which means that 7+8+9=D is the correct answer.

However, I'm not sure if this is correct or not, as the logic behind these types of puzzles isn't that complex usually, so my question is: Is my solution correct, or am I overcomplicating it so much that my solution actually is incorrect?

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1 Answer 1

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My immediate thought (and admittedly, I'm not sure I would've gotten it were it not for the example problem you provided) is that

7+8+9=R

and the reason why is that

1+2+3=6->siX
4+5+6=15->fifteeN
7+8+9=24->twenty-fouR

This, to me, feels more correct (or at least, less contrived) than your proposed solution.

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    $\begingroup$ "(or at least, less contrived) than your proposed solution" I guess that makes sense, since the solution didn't need to be that complex, it seems. $\endgroup$
    – CrSb0001
    Commented Apr 5 at 15:01
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    $\begingroup$ @CrSb0001 yeah, your solution is totally valid (all the logic makes sense and the math checks out). the problem with these types of puzzles is that there's so little information that it's often pretty easy to come up with multiple patterns that fit. usually, though, the intended solution is the one that is the least complicated $\endgroup$
    – juicifer
    Commented Apr 5 at 15:30

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