Jigsaws again

I know and I’m sorry. Here I am blogging about jigsaws again. You see they are so interesting as a parallel for certain aspects of human life. They are about finding patterns, sticking with it, rising to the challenge and, in the end triumphing over adversity. Well, having a bit of fun along the way, especially in the long and wet winter months.

There is something I find fascinating about them and they are one of my favourite pastimes. They achieve very little but do pass the time yet does it matter that not everything needs to achieve something?

One aspect that has fascinated me is the mathematics behind jigsaws. I don’t have the mind for it, at times I wish I did, but I have often wondered about probabilities relating to jigsaws. If you start with a random piece from the centre of a standard jigsaw then there are four other possible pieces that could connect to it. By my reckoning that means the chance of picking the correct piece at random would be 4 in 999. Not a big probability. 

After adding a second piece then there would be six possible pieces that would fit and so the probability would be 6 in 998. Now it gets interesting (really?) Adding a third piece depends upon where you put it. If it is inline with the other two then there are eight other possible pieces, yet if it creates an L shape then this number is reduced to seven. This gives either 8 in 997 or 7 in 997. 

The fourth piece gives three possible combinations, ten in a line (10 in 996) nine in an extension of the L shape (9 in 996) or eight if it is in a square. It seems to me that the possible number of combinations of prices depends upon the way it is put together. No wonder I can’t get my head around this. I don’t think there is a formula. Perhaps a mathematician out there could help me out.

The upshot of all this thinking however, is that I have attempted a new way of doing a jigsaw. I have simply laid out all the pieces, picture side up, picked one at random and building out from it. I started with a 500 piece puzzle, simply because the effort of laying everything out would have been too much with the full blown 1000 piece. So far it has been surprisingly easy, so much so that my mind has wandered once again to probabilities.