tag:blogger.com,1999:blog-5730391.post2444130140366755088..comments2024-03-28T18:08:45.225-07:00Comments on Blaine's Puzzle Blog: NPR Sunday Puzzle (Nov 6, 2011): Count the Equilateral TrianglesBlainehttp://www.blogger.com/profile/06379274325110866036noreply@blogger.comBlogger165125tag:blogger.com,1999:blog-5730391.post-33639265016092587972011-11-27T06:23:31.048-08:002011-11-27T06:23:31.048-08:00Everyone tried so hard to overthink this one, with...Everyone tried so hard to overthink this one, with all the mathematical equations and theories. Did anyone think about just simply counting how many equilateral triangles you could find -like the instructions asked? I drew the coins in Illustrator, then drew each set of triangles, a different color each, then... wait for it... COUNTED THEM. High School education (barely) and common sense got this one. That is why we are in so much trouble now as a country and worldwide: Too many SMART people trying to be too clever. My clue also referred to the (In the Year) 2525 song, "Guess it's time for the judgement day"Sizhttps://www.blogger.com/profile/02449426817613139276noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-87895807378585319472011-11-16T11:02:37.321-08:002011-11-16T11:02:37.321-08:00Maybe word the problem so the triangles can not ha...Maybe word the problem so the triangles can not have points made of intersecting lines. or must share all three vertices with the center point of the remaining coins. Nice video, I did the same method of counting small then mid sized and so on.Mr. Sidhttps://www.blogger.com/profile/09043170098192612106noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-531825416493292972011-11-16T00:23:32.149-08:002011-11-16T00:23:32.149-08:00Mr. Sid,
Indeed! To clear this up for everyone,le...Mr. Sid,<br /><br />Indeed! <a href="https://bitly.com/sQ6Y7u" rel="nofollow">To clear this up for everyone,let me re-emphasize the video I made that demonstrates the solution. View it by clicking here.</a>PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-27512343071697029682011-11-15T19:14:24.460-08:002011-11-15T19:14:24.460-08:00Should have read the post first. Started to count ...Should have read the post first. Started to count more and more. 174 it is.Mr. Sidhttps://www.blogger.com/profile/09043170098192612106noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-11412169019683768402011-11-15T19:01:34.668-08:002011-11-15T19:01:34.668-08:00For the Triangle coin puzzle. The 6 mid sized R-L ...For the Triangle coin puzzle. The 6 mid sized R-L Triangle make up 18 more small sized equilateral triangles.Mr. Sidhttps://www.blogger.com/profile/09043170098192612106noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-64164862143413344352011-11-15T18:51:48.089-08:002011-11-15T18:51:48.089-08:00is it not 43is it not 43Mr. Sidhttps://www.blogger.com/profile/09043170098192612106noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-78799058753717175892011-11-12T21:40:14.279-08:002011-11-12T21:40:14.279-08:00And pray tell, what is that number?And pray tell, what is that number?skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-21288441405731095152011-11-12T21:23:46.702-08:002011-11-12T21:23:46.702-08:00I think there is a number missing from the post.I think there is a number missing from the post.Bryanhttps://www.blogger.com/profile/11149525317349695429noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-77620624989450809802011-11-12T21:05:53.352-08:002011-11-12T21:05:53.352-08:00New puzzle just came up:
What number comes next i...New puzzle just came up:<br /><br />What number comes next in the following series: 2, 4, 6, 9, 11, 15, 20, 40, 60 and 90?skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-14684985190641403442011-11-11T18:32:13.091-08:002011-11-11T18:32:13.091-08:00It’s my hope that the number of comments garnered ...It’s my hope that the number of comments garnered here reaches at least, oh I don’t know, let’s say 174. (#156 here.)PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-30122645498538048172011-11-11T18:17:36.944-08:002011-11-11T18:17:36.944-08:00@RoRo, you are correct. This puzzle post has had t...@RoRo, you are correct. This puzzle post has had the most comments to date. The last time we had a similar response was back in May 2009 with a <a href="http://puzzles.blainesville.com/2009/05/npr-sunday-puzzle-may-10-another.html" rel="nofollow">deceptively difficult puzzle with numbers</a>. That puzzle was one comment short of breaking the 3 digit mark.Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-57382634175506729122011-11-11T18:04:30.914-08:002011-11-11T18:04:30.914-08:00Oh what the hay. Since I messed up on this one I ...Oh what the hay. Since I messed up on this one I feltI had to redeem myself by at least getting the Car talk puzzle tho I didnot (could not? too late?) submit the answer. I just felt that was the least I could do to hang in with this prestigeous group. Also impressed by the number of blogs. Don't think I 've seen so many in the last couple of years since I joined in the fun.Robin Thomas Poponnehttps://www.blogger.com/profile/05703107344880425239noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-80875906229832901022011-11-11T17:59:52.019-08:002011-11-11T17:59:52.019-08:00Just to quell suspicion that I’m engaging in flame...Just to quell suspicion that I’m engaging in flame bait here, let me just emphasize that I believe Will’s intent <i>was</i> for such an assumption to be embedded in the puzzle, and while it is very human of us to accept this belief as fact when solving the puzzle, it is a logical leap to do so.PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-50092857656784547262011-11-11T17:39:06.937-08:002011-11-11T17:39:06.937-08:00SDB:
I’m aware of the larger context of Will’s re...SDB:<br /><br />I’m aware of the larger context of Will’s responsibilities and am under no delusion that he could ever regularly dedicate time equivalent to our collective hours of thought.<br /><br />As to the heart of the matter, I am not claiming what is <i>likely</i>. Rather, I am observing that the logical conclusion that follows from the puzzle <i>as worded</i> results in 174 equilateral triangles. Whether our intuitions want to assume an embedded assumption that does not exist with regards to the placement of the triangle’s vertices (for the sake of simplicity or otherwise) does not change the fact that no such assumption is stated, explicitly or even implicitly, in the wording of the puzzle as given.PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-89092955475885029512011-11-11T17:18:04.393-08:002011-11-11T17:18:04.393-08:00I think it might be well to keep in mind that some...I think it might be well to keep in mind that someone in a position such as Will is, that he has concerns other than simply providing a puzzle for us to solve each week. What I mean is that he needs to protect his interests, which include keeping in the good graces of NPR and its' bosses. Therefore he will naturally be interested in generating as many positive email responses to NPR as he reasonably can. This will send a very strong message to those in charge that he and his puzzle segment are well attended to by the listeners. Because of these concerns he has nothing to gain, and everything to lose, by presenting obtuse puzzles that will only appeal to a very tiny minority of listeners. Because of this it seems obvious to me, Blaine (I believe) and others here that the more complicated puzzle is highly unlikely.skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-70992090132138187432011-11-11T16:37:57.834-08:002011-11-11T16:37:57.834-08:00Blaine,
I agree with your assessment that probabl...Blaine,<br /><br />I agree with your assessment that probably Will intended for the answer to be 25. However, whether this was his intention or not, it still remains that 174 is the most accurate interpretation of the puzzle as given, since the more rigorous condition of triangle vertices coinciding with coin centers cannot be assumed as it is worded—no matter how tempting it may be. As I’ve said, even I initially fell into this trap.<br /><br />I would hope Will at least acknowledges the validity of the larger result as following directly from the given wording.PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-30647121636934283172011-11-11T16:06:57.144-08:002011-11-11T16:06:57.144-08:00@PlannedChaos,
I agree that going with your alte...@PlannedChaos, <br /><br />I agree that going with your alternate interpretation leads to 174 triangles and that number has been confirmed by you, me and others that have checked your counting.<br /><br />However, given that Will is more of a word puzzler and since he likes to pick puzzles that you can be worked in your head or on a piece of paper usually, I think he intended for the triangles to strictly be those formed using the coin centers as their vertices. In his stating of the puzzle, I felt like he wanted us to think of points and lines not in the geometric sense but like one would in a "connect the dots" puzzle. Imagine the coin centers as dots. How many ways could you draw 3 lines (as in a segment joining two dots) to form an equilateral triangle? Using this way of thinking of the puzzle, I'm posting the answer as 25 triangles, but I do appreciate the effort you went through to enumerate all the equilateral triangles formed using the extension of line segments through centers. <br /><br />And as I said before I really do like your diagrams. My image editor is a little less useful when it comes to getting exact placement of points and perfect circles, but I did my best. :)Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-47614895931061466852011-11-11T12:57:56.001-08:002011-11-11T12:57:56.001-08:00Blaine,
I crafted the 174 frames by hand from the...Blaine,<br /><br />I crafted the 174 frames by hand from the Photoshop file I had made for the infographics, and then I compiled them as a 2 fps image sequence that I exported as a 1080 MP4 file in QuickTime.<br /><br />(Thanks again to Enya_and_Weird_Al_fan for the error checking on my set notation.)<br /><br />So, Blaine, are you convinced that the more faithful interpretation of the puzzle wording leads to 174 triangles rather than 25?PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-31900966033111259402011-11-11T12:31:04.423-08:002011-11-11T12:31:04.423-08:00@PlannedChaos, I'd like to know what tools you...@PlannedChaos, I'd like to know what tools you used for creating your graphics, both the original and the various lattice diagrams.<br /><br />For my "movie" I basically created several images and colored in the various triangles in each, then played them in sequence.Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-41543436652842825622011-11-11T10:51:47.748-08:002011-11-11T10:51:47.748-08:00I would remind Ralph Loizzo that ultimately we are...I would remind Ralph Loizzo that ultimately we are each responsible for the answer we submit. It is a puzzle game designed for those who are so inclined to see if they can solve the given puzzle using their own wits. It is always a little annoying for me when a "winner" for the week is chosen who did not even solve the puzzle herself, but discloses that she obtained the answer from her son who lives in another part of the country. I always wonder what posses such a person to submit an answer obtained in such a manner. To me this is unethical. Fortunately this does not seem to happen often.skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-9176072491326745052011-11-11T09:30:09.732-08:002011-11-11T09:30:09.732-08:00Wow - Now I want to know how that video was made.
...Wow - Now I want to know how that video was made.<br /><br />But this is why I hate contributing hints on Blaines. Because I was WRONG!!!!! And I'm sorry for anyone who followed my hints and were led astray.Ralph Loizzohttps://www.blogger.com/profile/16194974915716525500noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-76365866207477357772011-11-11T05:31:02.094-08:002011-11-11T05:31:02.094-08:00Blaine –
Great job on the video! You should defin...Blaine –<br /><br />Great job on the video! You should definitely let Will know ASAP if you haven’t already.<br /><br />ChuckChuckhttps://www.blogger.com/profile/13956539217339532507noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-74813533950429623752011-11-11T05:15:40.113-08:002011-11-11T05:15:40.113-08:00Enya_and_Weird_Al_fan:
Thank you for the error ch...Enya_and_Weird_Al_fan:<br /><br />Thank you for the error checking. I've updated the video appropriately to reflect your corrections. Yes, {BL-EJ-FL} was mislabeled as {BF-EJ-FL}; however, {AB-CK-EK} was not missing per se, I simply did not follow my own notation by including it as {AB-CG-EH}.PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-7794686564287120702011-11-11T03:53:13.231-08:002011-11-11T03:53:13.231-08:00I've made up an HTML file which divides all th...I've made up an HTML file which divides all the triangles found by PlannedChaos into individual groups based on in which of the four lattices they belong and then by size, compared to the smallest unit for a triangle within that lattice. I found out that PC mislabeled one and also missed one ({AB-CK-EK}). My HTML can be found at http://users.az.com/~jwaters/Puzzles/2011-11-06.htmlAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5730391.post-32411401483952650132011-11-11T00:15:40.454-08:002011-11-11T00:15:40.454-08:00I’ve created an 87 second explanatory video that s...I’ve created an 87 second explanatory video that shows the formation of all 174 equilateral triangles, which you can see <a href="https://bitly.com/sQ6Y7u" rel="nofollow">by clicking here</a>.PlannedChaoshttps://www.blogger.com/profile/12366856086658014260noreply@blogger.com