We all see these “intelligence tests” whizzing around facebook. Naturally they’re puzzles designed to make you feel smart, like many good puzzles in games are. You feel smart, so you share the puzzle. I design puzzles as part of my job, so I thought I’d dig into the design of a recent one that showed up on my feed. For best results, you might wish to attempt it yourself before reading on.

You start by doing the obvious addition, as guided. You check the number and soon notice that the number you’re looking for is contained within the “solution”. Let’s take 7+3 = 41021″. 7+3 = 10, and there’s a “10” hidden in that big number. It’s hidden behind just one digit. That’s the minimum number of digits required to throw you off at a first glance, while still making it as easy as possible to get there eventually. Once you’ve figured out this part of the problem, you automatically break the rest of the solution down into a “before” and “after”. For “7+3 = 41021”. The “4” is our “before” and the 21 is our “after”.

You now naturally check your two input numbers (7 and 3) and try to figure out how they can be messed with (the + indicates to your brain that they are both important) to get the ‘before” part with the first digit and the “after” part respectively. From there it’s simple trial and error in the three other basic operations. Most people try subtraction and multiplication first, and in that order because that’s the basic order of complexity (we don’t memorize division tables, we memorize multiplication tables).

The “solution” is helpfully ordered in the order of complexity as well, with the “before” mapping to the subtraction and the “after” mapping to the multiplication. Showing a large number of equations also increases the seeming complexity while actually providing you more information to work off with (lowering the difficulty while increasing satisfaction). It even uses math, which we associate with intelligence.

It’s a nicely designed abstract puzzle. Nice job to whoever put it together.