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Ideas. Insights. Inspiration.

Analogical Reasoning

Experience is valuable because it allows you to recognize something you've dealt with before and remember how you solved the problem at that time.


But it's especially powerful if you're able to combine it with analogical reasoning.


I'll demonstrate this truth using a "visual algebra" problem, the likes of which you've probably seen if you've spent any time at all on social media.

In the problem above, you're asked to solve for the "?" at the bottom of the puzzle.


Whether or not you've seen or attempted one of these puzzles before, take a moment to try and solve for "?" before you continue reading.


...


...


...


...


...


The correct answer is 44.


If that's the answer you got, congratulations: it means you're either very good at math and you're very perceptive...


... or you've seen these types of puzzles before and are able to learn from your past mistakes.


You see, while you might not have seen this exact problem before, it uses the same sort of tricks and traps that other visual-algebra problems tend to use.


And if you were able to recognize that this problem is similar to those other problems, you could have applied at least some of the same thinking to arrive at the correct solution.


That's analogical reasoning.


It takes practice, but it's a skill worth developing if you're in the business of solving problems.


And really, who isn't?



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Okay, if you didn't get 44 as your answer and you want to know how I did, I've outlined the solution below. Warning: if you keep reading, and you use analogical reasoning, it's very possible I'll ruin all of these puzzles for you from here on out. Of course, that's the point.


The first three lines are pretty straightforward:

  • Three identical bodybuilders equal 15, so each bodybuilder must be worth 5.

  • Three identical masks equal nine, so each mask equals three.

  • Three identical dumbells equal 18, so each dumbbell equals six.

The fourth line is where all the mistakes tend to happen.


The novice will see two dumbbells (i.e. 6 + 6), plus one bodybuilder (5), plus one mask (3), and believe the answer is 20.


But hold on... do those dumbbells in the final equation look different than the ones in the equation above? Absolutely. If you look carefully, you'll see that the dumbbells in the last line each have TWO plates per side, whereas the ones in the equation above have THREE! Each dumbbell doesn't equal six... each PLATE on the dumbbell equals ONE! (Yes, the plates are each different sizes, and in real life, the smaller plates would likely weigh less and thus should be "worth" less... but there's no way to accurately factor this into the equation, so we need to assume every plate is worth the same.) As such, the first value in the equation isn't 12 (i.e. 6 + 6)... it's eight (i.e. 4 + 4).


And wait a minute... does that bodybuilder look different? Absolutely. He's wearing a mask and carrying one dumbbell. You get partial credit if you noticed the bodybuilder's accessories... and full credit only if you noticed that the dumbbell he's carrying only has four plates on it (instead of 6). So the second value isn't five... it's 12. (i.e. 4 + 5 + 3).


But hold on... if you add eight and 12, you get 20. Add a mask (i.e. three), and you should have 23, right?


Wrong, because the last operator in the equation isn't a "+"... it's an "x".


And if at this point you get 60, well, you forgot about BEDMAS, which says you need to perform the multiplication operation first.


So what you actually have is this:

= (4+4) + (4+3+5) x 3

= (8) + (12) x 3

= 8 + [12 x 3]

= 44


That may not have been easy. But it should be much easier next time, right?

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