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There 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. :)

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.

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.

@John M.
–
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
–
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!

@John M.
–
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. :)

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestThere 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. :)

Log in to reply

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.

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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!

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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!

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And congratz on solving meh problem! :D

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Which is why I love mathematics. Only the truth counts in this realm. :)

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3141593??? Isn't that an approximation of $1000000 \pi$???

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P.S.. I'm not actually sure how many configurations there are yet.

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Badaboombadabing https://i.imgur.com/yGjvtUg.png

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