Row, Row, Row Your Trees
How can seven trees be planted so that there are six rows of trees in a straight line with each row having three trees? For example, if you plant them the following way you get only four rows of three (two horizontal, one vertical, one diagonal).
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Communicated by Jennifer Vahle ([email protected]).
Extra: With 10 trees, make five rows of four trees each.
Hint: remove one tree from the previous case.
I think the next is 19 trees, nine rows with five in each row.
Your email address doesn’t work; please email [email protected]
I DO DOT KNOW DA ANSWER TO ANY OF THEM!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
it’s a bit of a stretch but maybe the erdos distance problem?
https://en.wikipedia.org/wiki/Erd%C5%91s_distinct_distances_problem
I want to share this problem with my math club. Is there any topic I can teach that goes along with this problem?
possible
let me know if you want a hint ([email protected])
impossible
email to you bounced — please email sjm1 AT williams.edu
you can send me your solns and I’ll tell you if you’re right / if you need a hint
I do have a student/teacher corner that I”m slowly working on and I can share that too
I really like your website. Is there any possible way for you to send a copy of ALL of the answers to the riddles from this website. I am a mathematics teacher and would love to pick and choose and use the ones that I would like to in my classroom.
tough to tell from your formatting
are you counting the row of 4 as FOUR different lines of 3?
if yes this is very clever but it is NOT the ‘common’ solution — there is
a way to do it with each row of 3 having just 3 trees in it //s
PS: Sadly the formatting seems to be lost in posting. I’ve ‘fixed’ it for display purposes by leaving the trees as * and putting in _ elsewhere
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Hi – Anyone have any idea? 9 Trees can be planted in straight lines with just 3 trees in a line making (a) 9 lines and (b) 10 lines ?
glad you’re enjoying it /s
This site has received heaps of very helpful info on it. Thanks for informing me!
sent (but briefly, think symmetry) /s
Hint please haha!
no
may i count one row twice (count opposite direction) ?
sure, sent
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can i have a hint please
how many intersections do you have with the star of david? remember you can only have 7 trees….
Star of David with a tree at each intersection?
sure, emailed a hint ..s
can’t think of the answer, is it to much asked for some help?
Glad to hear you’re using these. Sure, will send along. Also, if you and/or your students want to help out or get updates about the student / teacher corner I’m working on, let me know. This’ll have solns, comments on how to attack them, connections to higher math….
We have been trying all of your riddles in our class, could you send me the solutions to help support them? Thanks!
I’ll send along a hint first, let me know if that helps
sure, will email
Can you please send me the solutions to your riddles….I am going crazy with these!
I am able to get to 5 rows of three trees. Any hints?
HINT (SPOILER): try an equilateral triangle with 3 trees at the corners and 1 in teh center. you need to figure out where the other 3 go….
Any other hint? Thanks!
Or else, please send me the solution before I loose more time on this 🙂
Yes, but they don’t (at least they don’t in my solution).
Can the rows have more than 3 trees in it?
sure
can you email me the answers?
If you want a hint, email me at [email protected]
I got the 7-5-3 one pretty fast but the others are a lot harder.
If you want a hint or me to check your soln, email me at [email protected]
hahaha i got it the first try! You shouldnt give the hint to easy oh wait unless diagnols dont count whoopsie daisys
I never tried it with fewer than 9. Maybe I should look into it 😀
Yep — there’s a nice way to do it with 9. Can you do it with 8, or 7, …?
And yes I was trying to say that with 9 trees, creating 10 rows is possible. Another problem for visitor to think about. Or if you like it, you can put it up on your website as well ^^
Can the trees be all in a straight line? That’d be 6 rows for you out of 7 trees?
not following — or are you saying this too can be done?
Another extra: 9 trees and 10 rows 😀 hihi
Very creative, but no. You can do it with each row having three and no more than three.
The only solution I see involves a row of more than three trees being counted as a row of three for each seperate group of three consecutive trees. For example, …. Would constitute two “rows” of three.