I’m going to start by talking about games. It may be a while before I talk about Problems. Eventually, I’ll get to video games. So, don’t be put-off if I start with something like Noughts and Crosses.
Some games we all know are considered children’s games. A few that spring to mind are: Noughts and Crosses; “One potato, two potato..” (the playground selection game); and, a variety of games where you take away a number of coins/pebbles and the loser/winner is the player who takes the last one.
If you were to ask an adult why they don’t play Noughts and Crosses, I Imagine many would say it’s because it’s “too simple”, “boring” or “too easy”. I’d argue that it’s the last of these which is nearest the truth. Noughts and Crosses is fun if you don’t know how to win, and most adults do know.
The counting games I mentioned are a little different. There are simple winning strategies, but fewer people know them. But, if you were playing the games for money every friday night, with a few drinks and nibbles, you’d soon learn them.
So, what about a harder game, like Chess? Chess remains interesting for adults because no-one knows how to win. (That sentence should probably have started with the words ‘I think that…’.) Note that I said ‘interesting’ rather than ‘fun’ – many people find chess “boring” and, presumably, those who can’t find a suitable opponent may also think it’s “too easy”.
By now, the nearest I’ve got to connecting (1)’Hard Problems’ and (2)’Good Games’ is to say that Chess is (1) a ‘Hard Game’ and (2) an ‘Interesting Game’. So, really, I need to bring in the words ‘Problem’ and ‘Good’.
So, Problems. There are lots of very hard problems which can be grouped under the heading ‘Packing Problems’. With these problems, you start with a container (knapsack, 2d-shape, box,…) and a bunch of ‘things’ of varying shape, size, weight etc., and you have to find the best or only way to put some or all of the things into the container, possibly satisfying some conditions.
If you just have a few ‘things’, and you know there’s only one solution, you can solve these problems by trying every possible combination (and arrangement) of the things until you get the one that fits, and then stop. But if you have lots of things, this is impractical, it would just take too long.
In my opening sentence, I mentioned various things that I intended to talk about, but I forgot a couple – Toys and Puzzles.
Packing Problems are good example of how a ‘Hard Problem’ can make a ‘Good Toy’, or even a ‘Good Puzzle’. A good and reasonably well known example of this would be the Tangram; another might be the humble Jigsaw Puzzle. Most people know good strategies for tackling Jigsaws which, along with guess-work and a few other things, allow Jigsaw Puzzles to be completed before the heat death of the universe.
But still, such puzzles require a good deal of time and patience. There’s a few things we need to do to get from ‘Good Puzzle’ to ‘Good Game’, and that will happen in Part 2.
Hard Problems and Good Games
I’m going to start by talking about games. It may be a while before I talk about Problems. Eventually, I’ll get to computer games. So, don’t be put-off if I start with something like Noughts and Crosses.
Some games we all know are considered children’s games. A few that spring to mind are: Noughts and Crosses; “One potato, two potato..” (the playground selection game); and, a variety of games where you take away a number of coins/pebbles and the loser/winner is the player who takes the last one.
If you were to ask an adult why they don’t play Noughts and Crosses, I Imagine many would say it’s because it’s “too simple”, “boring” or “too easy”. I’d argue that it’s the last of these which is nearest the truth. Noughts and Crosses is fun if you don’t know how to win, and most adults do know.
The counting games I mentioned are a little different. There are simple winning strategies, but fewer people know them. But, if you were playing the games for money every friday night, with a few drinks and nibbles, you’d soon learn them.
So, what about a harder game, like Chess? Chess remains interesting for adults because no-one knows how to win. (That sentence should probably have started with the words ‘I think that’, but that’s probably true of many other statements I’ve made.) Note that I said ‘interesting’ rather than ‘fun’ – many people find chess “boring” and, presumably, those who can’t find a suitable opponent may also think it’s “too easy”.
By now, the nearest I’ve got to connecting (1)’Hard Problems’ and (2)’Good Games’ is to say that Chess is a (1)’Hard Game’ and (2) an ‘Interesting Game’. So, really, I need to bring in the words ‘Problem’ and ‘Good’.
So, Problems. There are lots of very hard problems which can be grouped under the heading ‘Packing Problems’. With these problems, you start with a container (knapsack, 2d-shape, box,…) and a bunch of ‘things’ of varying shape, size, weight etc., and you have to find the best or only way to put some or all of the things into the container, possibly satisfying some conditions.
If you just have a few ‘things’, and you know there’s only one solution, you can solve these problems by trying every possible combination (and arrangement) of the things until you get the one that fits, and then stop. But if you have lots of things, this is impractical, it would just take too long.
In my opening sentence, I mentioned various things that I intended to talk about, but I forgot a couple – Toys and Puzzles.
Packing Problems are good example of how a ‘Hard Problem’ can make a ‘Good Toy’, or even a ‘Good Puzzle’. A good and reasonably well known example of this would be the Tangram; another might be the humble Jigsaw Puzzle. Most people know good strategies for tackling Jigsaws which, along with guess-work and a few other things, allow Jigsaw Puzzles to be completed before the heat death of the universe.
But still, such puzzles require a good deal of time and patience. There’s a few things we need to do to get from ‘Good Puzzle’ to ‘Good Game’, and that will happen in Part 2.
