Bleah. Standard blog disclaimers about how things never work out the first time.
I remember a big yellow book that helped me learn to write BASIC programs. Well, actually, it just had a bunch of BASIC programs you typed in and eventually I got frustrated with the unoriginality of it all and started modifying them, especially the ones where you played against the computer and the odds weren't even in your favor. Of course I wish I still had it, and of course the game I remember best is the one I thought I'd remember least.
I started off with the short programs, basically cool things to do with text(hangman, etc.) Nothing magical, no peek and poke, not even "Amazing chase" or "White Lightning"(my father wrote in games like that from a magazine he subscribed to.) There were the sports games I stayed inside on beautiful summer days to type up, and there was even NIM, which scared me so much I didn't even bother to figure out why it worked until I saw the solution on the wonderful site http://www.cut-the-knot.com. The solution was more interesting than the actual game, and I proved it with induction too once I saw the algorithm! I've come back to cut-the-knor for the slide puzzles that pop up as mini-games, and it clearly discusses which are solvable and which aren't. You'll probably find some canonical games you wondered about or saw in another context. These examples always get recycled for other thought mini-games.
But the game I learned most from was probably Hunt the Mugwump.
As a game, it was too dry for mass consumption, on a 10x10 grid, where you had five mugwumps and had to guess their location in ten moves. The computer gave the distance of each in square units from you. Once I got bored of stupid calculator tricks like noticing 1/7=.142857142857 and so forth(I remember a few minutes of intensive research verifying that it kept going) I tackled the weird weird numbers Hunt the Mugwump gave me. For instance if you were 1.414 units away, that means a mugwump was 1U/D and 1L/R. So basically you could take two points and pretty much know where all the mugwumps were, though I didn't know it at the time. I was amazed you could find them in under ten moves. Then I started being able to estimate the square of a number without my fancy little calculator with the red LCD numbers(I think my mother took away the grey screen one with the black numbers as I always used to push the screen to get rainbow colors.)
In fact with a little reasoning you can get things done in 7 moves. The solution is rather simple, and it involves actually two stupid guesses at first.
1. see the distances at (0,0) ie the bottom left corner.
2. see the distances at (1,0)
Call the squares of the distances d1-1, ..., d1-5, d2-1, ..., d2-5. A little algebra shows d2-1 - d1-1 = 2*(horizontal offset of mugwump 1) - 1. But if you know the horizontal offset you know the vertical. The trick is knowing the squares, or how to multiply the numbers in your head. Of course, you know that even though they are 7 digit decimals their squares are integers, so you can pretty much guess i.e. 6.403124 gives 64*64=4096 so the distance is probably 41, and the two squares that is a sum of is 5&4 so the mugwump is (+-4,+-5) or (+-5,+-4) away from that guess.
And of course it is not good enough to rely on #1. If the distance is 5.656856 then you know the location is (4,4) but this is a rare case. For D=5 it could be 5,0 4,3 3,4 0,5. Note that plot 2 would give distances of 4, 4.242, 4.48, 5.1(guesstimates) depending on where the mugwump WAS. For pretty much any point you have possibilities of (x,y) or (y,x) but of course you can't have 2 possibilities where x1=x2 as |y1|=|y2| but y1, y2>=0.
I never worked this last bit out beforehand. It seemed intuitive that I would start with the center, and I worked things out from there, sometimes using arithmetic, sometimes saying "the distance got greater, so the mugwump is over that-a-way." There's no question my stumbling around made it easy to figure out the solution when I thought about the game this morning. I think I expanded the game to 20x20 and tried to do it all in my head. It wasn't a great game, but it stays in my mind due to how it made this sort of reasoning fun.
Though it did make Number Munchers seem trivial for me when I pulled that game up just the other day. That'd be another blog entry. But I was amused at how, when reading about NM on wikipedia, I said, gee, I can go even more old school than that.
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johnny_cairo - July 26, 2007 (02:11 AM) We had a game like that called Hunt the Wumpus on those TI-80 computers. The carts were the size of eight-track tapes. The grid was exactly 10x10 and you only had one arrow to use. If you missed then you give away your position and you become a Wumpus snack. It was quite tense for something made 27 years ago. Also if you were good with that probability calculation, you'd remove the colored squares that give you an idea of where the Wumpus is hiding. "Invisible" mode. |
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aschultz - July 26, 2007 (09:42 AM) Hey there, long time no see! Wumpus turned up in wikipedia and I would guess that the programming book authors gave a slightly more forgiving game to someone who had to type it in in the first place. Maybe they changed the name for copyright reasons too. The other game I remember from this was a bowling game("push return to roll ball") where all pins were knocked down at random so you could wind up with a 1-5-7-10 split or something like that. |
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