Zee ("Da Gud"), Tobee ("Da Badd") and Luna ("Da Ugly") hav had a dispute and hav dasided tah settle id in a truel. Zee iz da worst shot, hitting 1/3 ov da tyme. Tobee iz twice az accurit, getting hiz target 2/3 ov da tyme. Luna iz an awezome markscat, nevah mizzing. Itz bin dasided da firing order iz Zee denn Tobee (if alive) denn Luna (if alive). Awl three r yntarezded in staying alive az long az pawzible and fire accordingly. If 2 or mowa r ztill purring at da end ov a round, da survivors goe anothah round. Intentionally mizzing iz allowed. Wat shud Zee's strategy be and what's da probubbillitee he'll survive?
Translation by http://primepuzzle.com/blog/jspeek.html
using a 1530 word dictionary.
6 comments:
I'll have to put my thinking cap on for a while and get back to you on this.
Hint:
Tah morphaphrase,
Blessed r da weak (οι πραεις) foah dey shall inherit da urth (κληρονομήσουσιν την γην ), egzpecialy if dey fuhst intentionally miss.
the word verification today is
"reste" as in reste in peace, little kitties. If these were my kitties, I wouldn't let them play with guns.
This little problem is not an easy one to solve. I'd like to pose a simpler problem that, once solved, will be a very useful in solving this bigger problem.
Let's concentrate on a duel right now. Let's analyze the chances Zee has for surviving a duel w/ Toby.
(Oh. BuBe's got a point, so I've decided to use paint ball pistols instead of real guns.)
Recall, Zee hits w/ probability 1/3 and Toby hits w/ probability 2/3. If Zee gets the first shot, how would you figure out the probability he will not get hit w/ a paint ball?
Here's an equation for Zee's probability of survival:
the probability Zee wins =
probability he hits Toby on the first shot + (probability he misses Toby on the first shot)*(probability Toby misses him on his shot)*(the probability Zee wins)
In our case, letting p stand for Zee's probability of survival :
p = 1/3 + (2/3)(1/3)*p
One equation, one unknown. I know, Algebra. Ughhh. But give it a shot.
I'm TcT's friend Mouzie and I think this blog is very awesome. I sure wish there weren't so much Algeebra tho. I do know, however, how to solve that stupid equation for p so if you guys need help, leave a comment and I'll tell you the answer.
Mouzie's blog is http://pccmath.blogspot.com/
It has just been updated and contains a screenshot of the latest version of the simulation of the truel problem and several other links that take you to the code behind it.
Improvements include:
1. finally got the colors right (the yellow dot is now actually yellow)
2. all numerator / denominator pairs are implemented using two element arrays (e.g. int nd(1) where nd(0) holds the numerator and nd(1) holds the denominator)
3. the program now asks you to supply the hit probabilities for the two weakest shooters
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