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.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .

Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.

Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold

- bulleted - list

bulleted

list

1. numbered 2. list

numbered

list

Note: you must add a full line of space before and after lists for them to show up correctly

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 Muradeli
–
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 Muradeli
–
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. :)

Easy Math Editor

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.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in`\(`

...`\)`

or`\[`

...`\]`

to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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.

Log in to reply

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!

Log in to reply

Log in to reply

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!

Log in to reply

Log in to reply

And congratz on solving meh problem! :D

Log in to reply

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

Log in to reply

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply