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Top Geometry Educators Catherine R. Missouri State University. Megan C. Piedmont College. Christine G. Cairn University. Maria G. Geometry Bootcamp Lectures A few Circle Theorems In mathematics, a theorem ….
Angles and Cirlce Theorems with chords and tangents In mathematics, the tangen…. Recommended Videos Problem 2. Problem 3. Problem 4. Problem 5. Problem 6. There are precious few such numbers that could possibly be the answer to this puzzle. BTW,I hope your observation is wrong, because I really don't want to recount the triangles!
For that reason and since we seem to agree on the actual answer I have to delete your post. First it might give somebody a clue directly to a triangle they missed. Additionally, it narrows the locations they might have to search to find a missing triangle. As for the labeling, feel free to use the revised labeling you've come up with. My method of counting really doesn't rely on labeling the interior vertices, just the 6 on the outside, but I'll switch to letters if you like.
Done, I'm using letters on my outside vertices, matching with your diagram. Also, I found it helpful to use the numbers 0 - 9 for the inside vertices. At 2 this afternoon I read Blaine's post that he'd just posted above in this thread and it almost made me give up, but now I'm glad I didn't. I haven't finished counting yet, but I think it's easier if you label the vertices with letters, rather than numbers, to avoid 2-character labels.
The task is to count all the valid 3-tuples. I've made a revised. Jan: Good advice, but I felt I needed a more stimulating challenge, which is why I labeled all mine with Roman Numerals.
I tried that, SkyDiver. Still not stimulating enough. So I connected the vertices with little cattle prods. Worked like a charm! Careful there, GBoy.
I'm an old frustrated cowboy and I long for the old days when a roundup was still called a roundup and not a steering committee. That's a great one, SDB. The first time I heard Garrison Keillor deliver that line, I laughed so damn hard, I nearly kicked the slats out of my baby crib!
AbqGuerrilla: Now you won't believe me when I tell you I came up with that joke myself years ago. I have never heard no pun intended it used by anyone else, but am not at all surprised as it is a formula joke. I have not used it that much, but when I have no one seems to have heard it by the way they laugh. I seem to recall that I even sent this joke to him a few years back, along with a few others I coined. I have not heard him use any though, but I usually don't listen to his show.
After the last one, my Eliot Spitzer joke, I mentioned that I make up my own jokes, to which an older woman from New York indignantly said she had heard that same joke from a New York cabbie. I said, "Did you really? I told it to many New Yorkers and none had heard it before, but all loved it and several insisted I tell it to their partner, spous, boss, etc.
One guy remembered it a year later when he returned to Seattle and asked me to tell his colleague. I am not surprised that it got around that way, but am surprised I have never heard any of my other well received jokes come back at me. Humor is a funny business. SDB: I totally get it. I write humor as well. And of course, from time to time, I have been known to borrow a line here and there I'll be using your "steering committee" gag line on next week's show -- but I am fairly sure GK used it in one of his dusty cowboy bits last year.
Unlike, GK, I will give you contributor credit at the end of the show. And, just for the record, I enjoy our banter and hope the feeling is mutual.
OK, enough of the sweet talk. It's much more fun to cross pens with you! AbqGuerrilla: Thanks Rush. Maybe GK did decide to use it. I had looked via a search in my email to see if I had sent it that way, but no emails to him with that joke came up. I also sent him jokes via the NPR website, so that may be it. I sent it because I thought it would be perfect for Dusty and Left Knee to use. I am really down on Garrison K. After many years in therapy, and finally beginning to feel adequate, along comes GK to inform me that I'm so lacking in whatever it takes to be a real human that I don't even know my sleep number.
Can you feel my pain? Here is one I sent that I thought would be perfect for his show: The major difference between George W. Bush and Bill Clinton is that Bush confers frequently with his generals, whereas Clinton paid more attention to his privates. Now, getting back to your email. I did not have banter with that poster! The biggest laugh in your posting was actually the "Thanks Rush" intro. Had you ever caught my program on the airwaves Thanks for the great graphic Blaine!
Indeed, I was again inspired to make a "count the triangles" video for this. Please ignore my comment posted last night about the answer being a prime number. It isn't. Didn't mean to lead anyone astray. Think I'll just finish harvesting my crop circles before the alien hex takes effect. Then I'll immerse myself in my little love triangle 'til next week. I have no doubt that a few retired computer squares from the Pentagon will come up with a program to figure this one out.
Meanwhile, please forgive my obtuse posting. I was unable to think of acute one. Not only have I failed at reaching the apex of the math puzzle world, but I fear I have fallen short of scalene any great literary heights as well. The Eskimos have an old saying: If it gets any colder we'll all be number.
Yes, and it has been so cold here in Provo this week that our local exhibitionist has just been standing on the corner describing himself. The funny part is that a not insignificant chunk of them are from this very blog : We now continue with our regularly scheduled programming Following his stated question there is no way to arrive at this answer without anagraming the result of replacing the R with an M.
I resent it when someone makes up the rules after the game has ended. I'm not sure Jan however it's pronounced and sdb correctly interpreted 'the funny thing', but I wonder if Mr. I can only hope it's not Ms. Duncan is chuckling about now.
That being said, if all or any of you want to 'Occupy Pleasantville', let me know, I might just be up for that. I've been going over it again and I think Paul may be correct and some others wrong, including my original conclusion. Count 'em again! To Enya, etc. Or perhaps you guys are over counting. I nave a new triangle count. So now I am going to commence counting sheep! Life is now back to normal. A very quick glance at a diagram of the puzzle while I was doing something else quickly solved everything for me.
I made a very stupid error when I first began working on the puzzle yesterday and never went back to double check on this one part. I am now laughing at myself big time. So, we are now in complete agreement you in the we group all know who you are and I am sending in my answer. I will wait until the deadline to reveal my goofy error so as not to give anything away to those who have yet to solve this puzzle.
Please save it for after the deadline. I appreciate the obfuscation, but if someone wanted to brute force it, there are a finite number of keys they'd have to try. I thought Will's explanation was rather confusing.
I don't know which line to omit. Only 55 right out of submissions! I've never heard such a low number! Any short diagonal where the endpoints are two apart would be fine.
He's just trying to make sure you don't pick a bisecting diagonal e. There is some helpful literature on this problem for the case when all the diagonals are included. After I read the article I was able to solve the puzzle as stated, and be confident that I have the correct answer. But I spent a fair amount of time on it, and regard the problem as non-trivial.
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