Sometimes when I am bored during lunch I dig out the paper and flip to the puzzles section. Crosswords don’t do it for me, I always look for target, the nine letter box thingo.
You know the rules, construct as many words as you can using each letter only once, and each word must contain the letter in the centre of the square. Sounds easy enough right? Most people are content to plow through, rattle off a few words and then give up. I usually try to go for the nine letter word, but always fail. Why is it so hard?
This is the difference between a normal person and a computer programmer. That question, “why is it so hard?” becomes a new game, all of its own.
There are only nine letters, there can’t be that many combinations right? Wrong.
Let’s start with three letter words. The first step is to take out the middle letter, ‘E’ (the example from the picture). We then have to pick two other letters to go with it, ‘F’ and ‘A’. How many different ways can we write them down?
Well there’s ‘AF’ and ‘FA’. After that you can stick the middle letter in three different positions, at the start, in the middle, or at the end. Three places for our two combinations gives six possible words, they being ‘EAF’, ‘AEF’, ‘AFE’, ‘EFA’, ‘FEA’, and ‘FAE’. None of those are real words, but we still had to try them.
Extending the same reasoning for more letters you come up with this:
Using 3 letters there are 6 possible combinations (3×2).
Using 4: 24 possible combinations (4x3x2).
Using 5: 120 possible combinations (5x4x3x2).
Using 6: 720 possible combinations (6x5x4x3x2).
Using 7: 5040 possible combinations (7x6x5x4x3x2).
Using 8: 40320 possible combinations (8x7x6x5x4x3x2).
Using 9: 362880 possible combinations (9x8x7x6x5x4x3x2).
Now it’s easy to see why finding those nine letter words is so hard. While a person won’t take the approach of randomly trying every combination it still gives a daunting idea of the search space they are dealing with. I also now understand why these puzzles are so common – it’s dead easy to write a computer program that generates them, so you don’t have to pay anyone to sit there and write them!
And that is the way my brain works. Rather than trying to play the game, I try to find the rules and principles behind the game. Unfortunately this approach doesn’t work in other areas of my life. Sometimes the principals are just too complex to grasp…