Pattern-finding is not merely a staple of one’s puzzle-solving repertoire, it’s a fundamental part of innumerable scientific, mathematical, and sociological discoveries.

From the Golden Mean and the Pythagorean Theorem to the Platonic solids and instances of symmetry throughout nature, our ability to discern patterns from the chaos all around us has helped to define the rules governing our universe.

Those a-ha! moments come in all shapes and sizes, from discovering previously unknown planets (by observing inconsistencies in established patterns) to the simple joy of puzzling out whether the five-letter word meaning “kingly” that starts with R and ends with L is “REGAL” or “ROYAL”.

This combination of keen observation and associative thinking is key to solving a lot of puzzles and brain-teasers.

For instance, consider the following numerical progression:

49 50 53 54 ___ 58 61 62 65

Pretty simple, right? Just add 1, then add 3, and repeat, making 57 the missing entry in the chain.

How about this one?

J F M A M J J…

What comes next?

While this one isn’t as straightforward as the numerical one above, the same parts of the brain are lighting up as you assess the possibilities, toss aside those that don’t fit, and conclude that these can only be the months of the year, and A, for August, would come next.

And here’s one that combines aspects of our previous examples, which I mentioned in a blog post last year:

In this zero-to-ten puzzle, place the missing numbers.

8 5 4 _ _ 7 _ 10 3 2 0

Now, if you started with mathematical patterns, you’d be stymied pretty quickly. -3, -1, blanks, -7, -1, -2. Nothing jumps out at you.

Then the associative brain kicks in, and you look beyond the numbers. What could they represent? Letters? Syllables?

And then the sheer simplicity of alphabetical order hits you like a freight train full of Scrabble tiles, and you instantly know where to place nine, one, and six.

Of course, there’s a flipside to such intuitive leaps. It’s called apophenia.

Apophenia is the spontaneous perception of connections and meaningfulness of unrelated phenomena.

This is the sort of thinking that fuels conspiracy theories and false positives in scientific data, assigning causality to coincidence.

One step beyond apophenia, you have pareidolia, a psychological term for the mind’s obsession with finding patterns in essentially random objects. When people see a face on the surface of Mars due to shadow and geography, or they see the Virgin Mary in the burn marks on a grilled cheese sandwich, that’s pareidolia at work.

It’s all part and parcel of being a pattern-finder. Some patterns reveal the underpinnings of the universe, others just reveal you’ve been staring at a tile floor a little too long. =)

Oh, and before I go, here’s one more numerical progression for the road. Enjoy!

242 121 123 41 ___ 11 15 3 8