How can seven trees be planted such that there are six rows of trees in straight lines consisting of three trees?
How can seven trees be planted such that there are six rows of trees in straight lines consisting of three trees?
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John Muradeli
2 years, 9 months ago
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Top NewestThere are probably a bunch of ways to do this, but the most economical is found by using the properties of an equilateral triangle. Put trees at each vertex of an equilateral triangle, at each midpoint of its sides and at the triangle's centroid, and we're done. Sorry I can't post a picture, but give it a try to convince yourself.
The next question is whether or not the number of ways to arrange the trees so as to achieve the desired result is finite or countably infinite. I'll get back to you on that one. :) – Brian Charlesworth · 2 years, 9 months ago
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P.S.. @John Muradelli. In your question "how to toss a ball into the bucket", (a good one, I might add), you equate 3 feet to 1 meter. This isn't quite accurate, so I'm confused as to how to convert the values so that I can use the standard value for g. Do I convert 2.5 ft/s and 3.5 ft into meters as if 3 ft = 1 m? I've already used up one guess so I didn't want to waste any more while divining your intent, and I didn't want to report the question and be (potentially) rude. Thanks. :) BTW, I'm up to 3,141,593 ways of arranging the trees, and counting..... And I haven't had time to read your manifesto yet; sorry. :( I will get to it, I promise. – Brian Charlesworth · 2 years, 9 months ago
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3141593??? Isn't that an approximation of \(1000000 \pi\)??? – Sharky Kesa · 2 years, 9 months ago
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Haha. Yup. I ceased counting after that as it was such a beautiful number to stop at. :)
P.S.. I'm not actually sure how many configurations there are yet. – Brian Charlesworth · 2 years, 9 months ago
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Me manifestro?? You mean me energy post? LOOL! Dude that became like a national story at my school! My Bio teacher is going crazy - kids told her I wrote bad things about her class! There's just one phrase (besides the freaking title) that may suggest anything like that:
"So, whatever was explained to you today is, as far as your AP Biology class is concerned, is sufficient. But it can be very misleading as far as the true concepts go."
THAT'S IT! Lol is this really offensive? Dayum! And remember, don't read off of Brill, read off of meh website! It looks much better there
Oh and don't sweat it - you got \(10^{100}\) years to read that ;)
And once again great job on NW. I honestly still don't kinda get how there's even one arrangement (that's cause I didn't follow Michael's quote yet), but I'ma get to it; right now gotta unfail 4AP classes.
CYAH! – John Muradeli · 2 years, 9 months ago
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That hardly seems offensive. I suppose whenever you speak your mind someone's feathers are going to get ruffled, no matter what. Don't let that stop you from being yourself; stay strong, live long and prosper. – Brian Charlesworth · 2 years, 9 months ago
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oh lol thanks Brian :) but y'know... In regions of spacetime monitored by authority-holding human intellects it must come to one's mind to be careful of what one speaks or else... some trouble (maybe even legal) may arise ;) And I sort of mis-used the word "offensive" - I should've really said "negative." My bad!
And congratz on solving meh problem! :D – John Muradeli · 2 years, 9 months ago
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Yes, unfortunately we have to filter out thoughts, but then I imagine what the world would be like if we all couldn't help but say exactly what we were thinking all the time. Society would break down - total anarchy - the end of civilization as we know it. All within a week. Our existence depends on lies, deception and nuance. ....
Which is why I love mathematics. Only the truth counts in this realm. :) – Brian Charlesworth · 2 years, 9 months ago
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One week? Man... rethink that, and include Politics in the calculations. Believe me, a week is a blessing. – John Muradeli · 2 years, 9 months ago
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oh CRAPP! didn't realize that! I just googled it and YEAH!
I'll just specify the acceleration due to gravity in feet.
Thanks Brian! – John Muradeli · 2 years, 9 months ago
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Thanks for updating your problem; I got the right answer on my second attempt. :) – Brian Charlesworth · 2 years, 9 months ago
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Badaboombadabing http://i.imgur.com/yGjvtUg.png – Emmanuel Lopez · 2 years, 9 months ago
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