The fact is, however, that the number of possible combinations is an almost completely useless number. It tells pretty much nothing about the complexity or difficulty of the puzzle. Moreover,

*increasing*the number of combinations (eg. by adding more pieces to the puzzle) seldom correlates to increased difficulty or complexity.

To understand why, consider this hypothetical simplistic "puzzle": There is a bag of 10 tiles, and each tile has a different number on it. Your task is to take all the tiles out in a random order and put them into a line. Now you have to rearrange the tiles one by one so that they will be in increasing order, from the smallest number to the largest.

You'd agree that this is a rather trivial and easy task. Not very difficult or complex.

But there are 3.6 million possible combinations of starting positions! Surely that must be an indication of how complex and difficult the puzzle is? Well, no. That number is completely meaningless. The puzzle is completely trivial regardless of the "3.6 million possible combinations".

How about we use 20 tiles instead? Now the number of possible initial positions grows to 2.4*10

^{18}. That's a staggeringly large number! That's 2 with 18 zeros after it! Surely the puzzle is now impossibly complex!

Well, no. The difficulty of the puzzle didn't increase in the slightest. The solution is still exactly the same, and exactly as easy. The only difference is that now it takes a few seconds more on average to "solve" it.

And that's precisely the crux of the problem: With many puzzles, increasing the number of pieces (and thus growing the number of possible combinations exponentially) often does not increase the difficulty or complexity of the puzzle at all. The only thing it does is to make it slower to solve (which oftentimes translates to "more tedious".)

Thus, in many cases, and quite ironically, a larger number of combinations is actually a bad thing. It doesn't increase the challenge of the puzzle, only its tediousness. The only thing that it may challenge is your patience.

Yet people still keep spouting these numbers like they had any kind of significance or meaning.

## No comments:

## Post a Comment