A 24 Game card



You certainly know the popular 24 Game, in which you're given four 1 to 9 numbers and the objective is to come up with some combination of arithmetic operations that will end up using all the numbers and which the result is 24. In my country there are (or used to be) some serious tournaments around it and I had the chance to reach a regional stage of the national tournament when I was in my 6th grade. However, my school didn't had that much cards so my training was limited because no matter how good you are at math the memory part of the brain will always reach the solution to a puzzle before the arithmetic part does a single operation, so having less cards means less memorization/training.

So recently, as my brother now reaches that level I just thought I could put in practice my programming skills (which would have been very helpful if I had them back then) and generate all the possible cards for that game. The program returns exactly 195 390 unique cards and presents the way of solving (there could be others). Just take it, memorize it and do your best if there are some tournaments you can participate in.

Click to browse all the cards

EDIT: My friend Pedro Diogo (many thanks to him) took the data and created ready to print cards. So,

Click here to download the ready to print cards.

 

If you want to check out the code feel free to here.




I don't know how you define a game. If it's just a word that defines everything that can be done to entertain and spend some time on then of course Sudoku is a game, but my definition of game is a bit different.

For me a game, above all, is something challenging, but not a dumb challenge, is some that requires Human's best quality to solve: intelligence. Does Sudoku require intelligence to solve? Or does it just turns us in some fancy ZX Spectrum computing all the way till the solution of the puzzle?

I've done recently a computer program that solves Sudokus, as it was the semester project of some subject of mine at college. And one thing that comes out at the very first analysis is that no really intelligently challenging game would have been easily solved by a computer program done by people that may have start coding 3 months ago.  There's really no artificial intelligence algorithms needed nor some other fancy techniques. You've just to dumbly generate all possibilities according to the rules and the numbers you may already have in the puzzle and test to see if a valid solution comes up.

So my thesis here is that what an human does to solve Sudokus is one of the most unchallenging things, simply turning an intelligent person in some Pentium, involuntarily generating all the possibilities for each square and for all the possible consequences of the move.
Difficulty of a Sudoku is made by putting less numbers in the puzzle and if possible not on the same row/column/block. All this just makes the human compute even more possibilities, making him go back and forth some times like a Depth First Search algorithm does to solve this kind of problems.

Of course there are lots of games that can be solved or played by a Computer, Chess is one of the most popular ones. But Chess is unpredictable, and no computer could easily generate all possibilities of game based on a move because there would be so many that it couldn't be able to process it, so it's required a bit of AI's help. Artificial Intelligence... as our logic can predict, if some of AI techniques are present in a program that solves a game, it seems that the computer really needs some of our best quality to solve it. If a computer needs it, we surely use it when playing. And that's the game we should play.

P.S.: for all the LEICianos in the place, solve Global's Cross-Words instead. :P



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