However, there are a number of different formulas that can be used to calculate the number of triangles in a given space, such as the Herons formula or the Eulers formula. Are there: Youll find 38 triangles here; check out the animation to see them all! Ready to give it a try? it seems that Type -3 formula fails in case if horizantal and vertical lines are same in a triangle, bro for this your assumption and tricks are good to solve but what to do when all the above are jumbled to single diagram or some another diagram (example is civils prelims triangle sum ). Simon Beale Heres How to Solve the Puzzle, https://www.nytimes.com/2019/08/21/science/math-equation-triangles-pemdas.html. How many triangles can you find? Sadly, that answer is incorrect. of triangles and combine squares having 4 no. Can you solve this triangle puzzles? How many non parallel lines are there to create a triangle? The original tweet received over 3,800 retweets and thousands more comments in response, as Twitter users pondered between themselves as to what the answer could be. What is dead flat paint finish, and when should you use it? Kumar Ankit, an engineering student from India, designed and posted this geometric puzzle to Quora, challenging users to find all the hidden triangles in this image (nothing goes super-viral like a controversial shape). Check out the animation that proves it. This shape has 14 triangles in it. The area of the triangle is 9 square kilometers. To put it another way, 13 is the correct answer. Youll find a total of 18 triangles in this image, looking at the thin, vertical triangles as well as the triangles made by the individual rowsand the combinations thereof. According to the picture, there are in fact 18 triangles hidden within the drawing . How many triangles? This content is imported from twitter. I never specified to only use those dark blue lines, and thus, I am wrong. Just go by size. With essay counting, there is no escaping the consequences. The puzzle also provided an intriguing brain teaser for those who attempted to solve it with a wide range of answers, its difficult to determine the correct answer. One way is to count larger triangles. If not, this animation will reveal them all to you. Others might notice that there are a few medium-sized triangles within the large main shape and cap their answer at 7. EGD is a 13 square-kilometer triangle formed by 13 triangles. Geometric optical illusion art distinguishes itself. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". Wellmaybe not. And if you want to delve deep into the math, you can check out the discussion on Quora. Click the answer to find similar crossword clues. Being an educator these days is a challenging experience. So now, divide out the redundancy. Required fields are marked *, Seth MacFarlane narrowly avoided death when he missed Flight 11 on September 11, 2001. listeners: [], There are three triangles in the outermost layer. Want more shape related puzzles? Hint: Here having total two diagonals and having eight blocks. Triangles of size 1 (as in 1 small triangle): 16 Triangles of size 16: 1 (the big triangle) Triangles of size 9: 3, this is pretty clear. How Many Triangles Do You See? Learn the Answer | Reader's Digest r/puzzles on Reddit: How many triangles do you see? It's supposed to be How many triangles are in this bigger triangle? Our readers have debated the problem for over 2 years. Martin Silvertant, a mathematician, created a diagram that explains where the 24 triangles are located. Heres how it works. The you have to add the same triangle numbers but skipping one (1, 6, 15, 28..378, which total is 1925) that represents the triangles down) So total number of triangles are 4060+1925=5985 . square, rectangle, rhombus, parallelogram, quadrilateral and trapezium, How many squares and rectangles are there in this picture | All Math Tricks, Integral and Double Integral calculus Example with Solution | Allmathtricks, Twos complement steps | Conversion of decimal numbers or binary number into 2s complement with examples, Pyramid Geometry Formulas and Properties | Frustum of Pyramid, Centroid of the triangle formula with examples | coordinate geometry, Coordinate geometry introduction | Locating of coordinate points, Frustum of cone formulaswith examples | Surface area and Volume, Surface Area and Volume of a Prism Formulas, rectangular and triangular, Surface Area and Volume of a Cone formulas with examples Allmathtricks, Volume and Surface Area of a Cylinder Formulas Right Circular Cylinder, Surface Area and Volume of Sphere, Hemisphere, Hollow Sphere Formulas, Examples. Sponsored links. Now the answer to the tricky triangle puzzle has finally been revealed after a clever photo surfaced on Twitter. Manage Settings Six lines create 20 triangles in total (6*5*4)/6, or 20 triangles total (6*5*4). pic.twitter.com/MCLcmL4Zie, Gergely Duds Dudolf (@thedudolf) December 20, 2015. Heres another one with owls. Picarats: 40. advertisement. Begrudgingly, I decided to take one last stab at figuring out just how many additional triangles there could be given our new chaotic rules, and arrived at 43, for a total of 61: Im quite sure, however, that someone reading this will very quickly tell me Im wrong yet again and deliver proof of even more hidden triangles, sending me down another rabbit hole on the long and winding path to eventual insanity. An even more nitpicking Quora user noted there was another triangle in the image if you count the word triangles. Less than 1% of people can ace this shapes brainteaser (though we bet the aforementioned eagle-eyed user is among that statistic). Figure 2 : Number of triangles in Fig 2 = 16. your blog for these tricks is really helpful for me. I dont think Ive ever met anybody whos counted right, Dr. Loh said. We recommend our users to update the browser. n factorial, when said aloud describes the product of multiplying all the integers from 1 to n. So 1! There are six triangles in the next layer. You can use the same procedure for multiple lines. If the vertices of a triangle are different from one another, the size of the triangle remains constant. 3.1K views 3 years ago #BRAINGAMES #RIDDLES #BRAINTEASERS How many triangles do you see in this picture in this "Count the Triangles Puzzle" ? A good equation is more than a recitation of rules; it expresses why those rules exist, reveals patterns and points to new problems to tackle. I have derived some of them using combinatorics. How many triangles? And one with snowmen. Reader James Goodrich took it another step further, suggesting we open our minds to consider what a triangle could be: I did, James. How about 2,300 lines? event : evt, The Rubiks cube has been maddening people for 40 years. There are 16 circles in this picture.https://t.co/PZ3s9t7gBD pic.twitter.com/TnuUoxe6dT, rebecca roache (@rebecca_roache) August 5, 2017. Reader Poingly, meanwhile, wrote in to say weve been making a grave error in counting the triangles all along: Outstanding point, Poingly. answer. POBODYS NERFECT in Canada (@davegrapes) May 10, 2017. A popular version of this puzzle states that there are 4 possible answers: 7, 9, 13, and 21. The artists signature is visible on the 25th triangle, which is a quarter of the size of the entire shape. The consent submitted will only be used for data processing originating from this website. of triangles lesson. Brainteaser: How many triangles can you find in this puzzle? We are no longer supporting IE (Internet Explorer) as we strive to provide site experiences for browsers that support new web standards and security practices. This figure represents 2,025,189,100 units. Now heres the catchcount how many triangles are in the drawing. Heres a handy breakdown of how to find each possible triangle: Johanna Mangahas, Ph.D., an assistant math professor at the University at Buffalo, also came to 18first through simple brute-force counting, then through the same crafty combinatorics as abovebut admits our triangle brain teaser isnt quite as cool as this one from Po-Shen Loh, Ph.D., a math professor at Carnegie Mellon University in Pittsburgh, as featured in the New York Times last year: This one has a slicker mathematical answer, she says, because here, counting triangles is the same thing as counting combinations of three lines chosen out of six [6-choose-3 = (6*5*4)/(3*2*1)]. 1. Count or Create The total number of triangles created by those six lines is (654)/6, or 20. The cookies is used to store the user consent for the cookies in the category "Necessary". How many triangles puzzle | How many triangles in this picture What about 23 lines? Watch the video for all the details. Your email address will not be published. How would you solve this equation and what answer do you think is best? Or, try moving on to these math riddles that only the smartest can solve. In the picture I sent her, some lines are parallel, so they cant be part of the same triangle. Just think of all the cool things that are shaped like triangles: slices of pie, tortilla chips, cheese wedges, the yellow bird from Angry Birds, and the cover of Pink Floyds Dark Side of the Moon.. Which is to say, if you forgot the formula, you can reconstruct it by remembering what its supposed to solve. 6+3+6+1=16 triangles. We may earn commission from links on this page, but we only recommend products we back. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. What are the lines approximating 2,300? For each puzzle, youll see a large shape with a bunch of lines drawn through it to form smaller shapes. Behold: That kind of dedication is just one of many reasons I love Popular Mechanics readers. trivia questions only geniuses will get right, spot the cat hiding among the bats in this image, Do Not Sell or Share My Personal Information. Did this one trick you into thinking there were more? If you took the same seven lines and shook them up a bit, probabilistically theyd most likely land like [Lohs] problem and youd have more triangles and a similar cute answer. (For the record: 35.). There are six possibilities; likewise, any triangle in the diagram could be created six possible ways. So many shapes! Put balls of six different colors into a bag. Thank you Mr.Sai for your valuable comment on this article, Really loved it. Thats the answer. answer. Counting triangles puzzle #4 | How many triangles are there in the How many triangles are there in each of the below images? You can see an illustration of all 24 here if you dont trust me. How Many Triangles Do You See - Viral Math Problem Triangle Everyone has a chance to win a valuable prize by completing the triangle puzzle. The good news is that this confirms that life clearly DOES have meaning, as evidenced by the. How Many Triangles Do You See? The answer is lucky number 2425 if you want to get fussy. Very nice and helpful tricks. Theyre a piece of cake to identify, right? answer. Let's start by counting the number of small triangles; the triangles that do not have any lines going through them like this blue one: 2. Then, count the number of triangles in the next layer. To solve the problem, start with this observation: Any three lines in the diagram define one and only one triangle. Thus, the total number of ways you can choose the sides of the triangle equals 654, or 120. I havent shared this new triangle problem with my coworkers yet. On Twitter and in the comments on The Timess website, it was clear that some readers knew immediately how to solve the problem because they had learned combinatorics, an area of math that figures out the number of ways things can be shuffled. Here is a similar puzzle, except with squares. And see if you can spot the camouflaged animals hiding in these photos. How Many Triangles? | Pub Quizine It also reveals that other problems are, at heart, identical. This video shows the best way to solve these puzzles. Puzzle Author: Stephen Froggatt See this puzzle without solution 25/07/2020. Here are some of the highlights: Sponsored links. I could have made this much easier on readersand, crucially, much easier on my inboxhad I just sketched the triangle on plain, white computer paper. If anyone else posted it, it'd probably be +5 at least. The base of the triangle will then have to be one of the three levels below. Seth MacFarlane Missed a Doomed 9/11 Flight, 1990s Odd News: Too Cool to do Drugs Pencils, About That To All You Hunters Newspaper Clipping, City Council: Library Cat Is Evicted From Home Of Six Years, British Firm Creates Putrid Comet-Smelling Perfume, Not Real: Jessica Alba Atlantis: The Lost Empire Remake, Five Movies That Inspire Students and Teachers, Google Image Search Salutes Atari Breakout, 9 (6 small red + 6 small white) or (6 small red + 3 medium, but no large), 12 ( 6 small red + 3 medium + 3 small white), 13 (6 small red + 3 medium + 3 small white + 1 large). Time for the final challenge, and its a doozy! Also remember You dont have to round off the number for example answer may come 36.8 then consider only 36. Were curious people by nature, but we also collectively share a stubborn insistence that were right, dammit, and so we tend to throw work by the wayside whenever we come upon a problem with several seemingly possible solutions. This may include 3 medium triangles which include three red and one white triangle along with a large triangle which encompasses the entire illustration, as shown below: Finally, we might want to count the three small white triangles. Shapes puzzle #1: Answer: B. Calling all brain teaser aficionados: This triangle trick (and no, its not an optical illusion) is sure to baffle even the most astute of brains for at least a few minutes. Godspeed. Andrew Daniels is the Director of News forPopular Mechanics, Runner's World, Bicycling, Best Products, and Biography. Any triangle we find in the drawing should have one top vertex and two others on the same horizontal line, so for each horizontal line, the number of triangles with two vertices on that line is equal to the number of ways we can choose these vertices, Bonahon saysnamely the number of ways we can choose two distinct points out of n, or n choose 2.. There are *SPOILER ALERT* a total of 24 triangles in this puzzle. YET ANOTHER TRIANGLE UPDATE 1/31/20: Since posting the last update, Ive heard from even more of you, continuing to chide meand your fellow readersfor not considering additional possible triangles. Your email address will not be published. If picture puzzles are more of your thing, see if you can find the hidden objects in these pictures. Can you please add their derivations also? Oh, right, a brain teaser. Thanks for your efforts sir. How Many Triangles Can You Find In This Picture? - Simplemost Number of triangles with side 1cms: 10 (1+2+3+4 upward facing) + 6 (0+1+2+3 downward facing) Number of triangles with side 2cms: 6 (1+2+3 upward facing) + 1 (downward facing) Number of triangles with side 3cms: 3 (upward facing) Yes, less thanone percentof people aced it! puzzle - How many triangles are there? - Mathematica Stack Exchange That equates to 23/22/2021/6. Working in a field which demands an intrinsic desire to help students while trying not to be taken advantage of by a society which does not value its teachers can be a delicate balancing act. But opting out of some of these cookies may affect your browsing experience. The tool will show you how many triangles are there. Puzzle 016 - Triangles and Ink. How many triangles are there in each of the below images? to this, as well as a few guesses not suitable for all audiences. An example of data being processed may be a unique identifier stored in a cookie. } Heres a smaller triangle to decipher. Are you up for the challenge? Number of triangles with side 2 cm = 1 + 2 (triangles facing upwards) + 1 + 2 (triangles facing downwards = 6 triangles Today we take a closer look at his brush with death. As a subscriber, you have 10 gift articles to give each month. of triangles. answer. (actually three: one obvious, one less, third one even less.) The total number of triangles is given by floor ( n ( n + 2) (2 n + 1)/8), where floor means to round down the resulting quantity to the nearest whole number. A couple of weeks ago, I wrote about a viral math problem 82(2+2) = ? It can be written as C(6,3), which is read as 6 choose 3. More broadly, its mathspeak for the number of ways to choose 3 items out of 6. https://twitter.com/twitersgoodboy/status/862086751480885248, Along with Suck it dork, incorrect answers ran the gamut from this, https://twitter.com/TheOrchidShow/status/862237105405218816. This cookie is set by GDPR Cookie Consent plugin. IMPORTANT UPDATE 1/30/20: Since publishing this story, many, many readers have reached out to let me know that while 18 is indeed an acceptable answer to this problem, it isnt the only one, due to some unintentional oversight on my part. A triangle of 13 squares has a diameter of 20 squares. Finally, I am here happy to find valid and correct answers, and also methods to do it in the right way. B.O.B. Many crossword puzzles feature complex clues that require special skills to solve. Hey, speaking of triangle mysteries, here is a brain teaser recently posted by Quora that has been making the rounds on the internet lately. equals 1; 2! The first part n!/(nr)! Its convenient to generalize to the case where there are n lines passing through the top vertex, and p horizontal lines, says Francis Bonahon, Ph.D., a professor of mathematics at the University of Southern California. To put it another way, 13 is the correct answer. Unfortunately, that answer is also wrong. If you can solve Kumar Ankits brainteaser in math, the problem should be relatively simple. 2019 Coolmath . (Heck, some people answer their own vaguely worded puzzles 5 minute after posting and get +15) $\endgroup$ - Quark. (new Image()).src = 'https://capi.connatix.com/tr/si?token=38cf8a01-c7b4-4a61-a61b-8c0be6528f20&cid=877050e7-52c9-4c33-a20b-d8301a08f96d'; cnxps.cmd.push(function () { cnxps({ playerId: "38cf8a01-c7b4-4a61-a61b-8c0be6528f20" }).render("6ea159e3e44940909b49c98e320201e2"); }); However, if you really want to get technical, the truly correct answer is 25. EBDs form triangles with an area of 6 meters. Nope, its not as easy as it seems! .css-v1xtj3{display:block;font-family:FreightSansW01,Helvetica,Arial,Sans-serif;font-weight:100;margin-bottom:0;margin-top:0;-webkit-text-decoration:none;text-decoration:none;}@media (any-hover: hover){.css-v1xtj3:hover{color:link-hover;}}@media(max-width: 48rem){.css-v1xtj3{font-size:1.1387rem;line-height:1.2;margin-bottom:1rem;margin-top:0.625rem;}}@media(min-width: 40.625rem){.css-v1xtj3{line-height:1.2;}}@media(min-width: 48rem){.css-v1xtj3{font-size:1.18581rem;line-height:1.2;margin-bottom:0.5rem;margin-top:0rem;}}@media(min-width: 64rem){.css-v1xtj3{font-size:1.23488rem;line-height:1.2;margin-top:0.9375rem;}}Why No Humanoid Hobbits Are Still Living, What Makes Ohio-Class Submarines So Badass, 6 Tips for Installing Your New In-Ground Pool, The Future of Mobile Military Power May Be Nuclear, We Built a Cool Mid-Century Influenced Desk, How Lasers Will Soon Power U.S. Military Bases, South Korea Is Building an American Arsenal Ship, Theres an Anti-Universe Going Backward in Time, Why France Is Still a Formidable Nuclear Power, 3 Simple Ways to Remove Wax From a Candle Jar. How Many Triangles Are In This Picture? Sunday Puzzle See the animation for this puzzle here. How many triangles are there in total? Meghan graduated from Marist College with a Bachelor of Arts in English in 2017; her creative nonfiction piece Anticipation was published in the Spring 2017 issue of Angles literary magazine. More challenging than it looks, right? Your goal is to correctly count how many of a certain type of shape are present inside the larger shape. If youre up for another challenge, try these brain teasers that will leave you stumped. In other words, both the pictorial triangles and the words referring to triangles are referents to the concept of a triangle, said Silvertant. Bonus question: How many quadrilaterals? The picture had 4 triangles and so we solved for the fourth term of 27. (232221)/6, or 1,771. Most people on Quora agreed that the answer is 24, with each row containing six triangles. Copyright 2008-2016 Wafflesatnoon.com, Inc. Theme by MVP Themes, powered by Wordpress. Location: Speak to Rodney in the Town Hall. How Many Triangles Puzzle Printable | Sally Crossword Puzzles Mathematicians reveal the real answer. answer. In our case, n = 4, and p = 3. How Many Triangles Are There Puzzles With Answers | Genius Puzzles { equals 321, or 6. The use of an equation conveys the idea behind a rule, as well as revealing patterns and pointing to new problems. The triangle ABC in this image is 6 square meters in size. Let's take a look at the graphic in question: There is a minimum of 6 small red triangles, though that isn't always given as an option. Heres how to solve the puzzle using the instructions. Jumble the digits every which way: 123, 132, 213, 231, 312, 321. You can find her byline on pieces about grammar, fun facts, the meanings of various head-scratching words and phrases, and more. Dont believe its that many? of triangles. Our Solution: 64 Triangles. That's fine, but we're just trying to solve this simple problem here, not the full generalization of it. callback: cb The image shows a large triangle broken up into smaller triangles: Can You Figure Out How Many Triangles Are in This Picture? So now, divide out the. The same calculation applies regardless of how many lines are used. Anyone, from toddlers to seniors, can create an optical illusion at home. 9 of the triangles in a triangle are formed by the triangle FBD. If youre in the mood for another puzzlebecause, hey, right not?heres one that made the rounds on the internet from Wheel of Fortune earlier this year. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. We recommend our users to update the browser. This fast-paced 3-D puzzle game involves a combination of quick thinking, logic, and luck to stack your spheres to earn the most points. What is your answer? The answer is 25!. Its the same triangle whether you choose line 1, then line 2, then line 3; or line 1, then line 3, then line 2. Please keep going sir , thanks you for such a awesome blog it is gonna to be really helpful, 11 th question under how become 3rd horizontal, Your email address will not be published. Jan 14, 2015 at 2:30 . Let's take a look at the graphic in question: There is a minimum of 6 small red triangles, though that isn't always given as an option. You can see an illustration of all 24 here if you don't trust me. We then posed the problem to our Instagram followers, whose replies also ran the gamut, from 5 to 14 to 37. The answer is might seem glaringly obvious now, but the brainteaser had everyone scratching their heads. There are a variety of solutions, depending on how you look at it. Plus, for more fun puzzles that test your ability to spot things, see if you can find the difference in these tricky photos. Crossword Puzzle, How To Solve Sudoku Puzzles: A Beginners Guide. The only way to form triangles in the figure I drew, Erikkson-Bisque says, is if the top vertex (corner) is part of the triangle. Life has no meaning.. 20, of course. Hana Hong is a journalist/storyteller who writes for Reader's Digest, InStyle, CollegeFashionista, Her Campus, and The Fashion Network, among other publications. Type 3 : Counting triangles with the Triangle having number of bisects with vertex and horizontal lines, Count the number of triangles in the above picture, Figure 9: Triangle counting in Fig 9 = 2, Figure 10: Triangle counting in Fig 10 = 6, Formula : Here number of vertical parts n and horizontal parts m then possible triangles is, Figure 11: Triangle counting in Fig 11 = 30, Solution : Here number of vertical parts 4 and horizontal parts 3 then possible triangles is 4 x 3 x 5 /2 = 30, Figure 12: Triangle counting in Fig 12 = 45, Solution : Here number of vertical parts 5 and horizontal parts 3 then possible triangles is 5 x 3 x 6 /2 = 45, Type 4 : Counting triangles with in embedded Triangle, How many triangles are in the above figures, Figure 13: Triangle counting in Fig 13 = 5, Formula : Here number embedded triangles in outer triangle n and horizontal parts m then possible triangles is 4n + 1, Figure 14: Triangle counting in Fig 14 = 9 ( Here n= 2 ), Figure 15: Triangle counting in Fig 15 = 13 ( Here n= 3 ), Type 4 : Counting triangles with in the particular pattern of Triangle, How many possible triangles are in the above figures, Formula to count number of triangles like above particular pattern type of Triangle, where n = number of unit triangles in a side. Why Trust Us? Hint: Here each square having 8 no. For another deceptively simple math challenge, see if you can pass this elementary school math test. This website uses cookies to improve your experience while you navigate through the website. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); My self Sivaramakrishna Alluri. Counting will get you nowhere. How? Type 2 : Counting triangles with the Triangle having number of bisects with vertex, Count the number of possible triangles in the above figures, Figure 5: Number of possible triangles in Fig 5 = 1, Figure 6 : Number of possible triangles in Fig 6 = 3, Formula : Here number of parts n then possible triangles is n (n+1) /2, Figure 7 : Number of possible triangles in Fig 7 = 10, Hint : No of parts n = 4 so according to formula 4 x 5 /2 = 10, Figure 8 : Number of possible triangles in Fig 8 = 15. Thats n(n-1)/2. How many triangles are created. This cookie is set by GDPR Cookie Consent plugin. How to grow ranunculus so you can have gorgeous bouquets all summer. Since there are six lines, there are six choices. People are scratching their heads at the different numbers they are coming up with (something similar happens with this viral duck riddle). Details. Also, see if you can spot the cat hiding among the bats in this image. For another challenge, see if you can find the turtle hiding among these lily pads. Brainteasers puzzle only for genius with answer! At first glance, the image seems to be a simple illustration with multiple. It is your responsibility to find the words that match to fill in any missing squares. Nope, there are only 15 triangles here (because, well, thats still a lot)! Thats (765)/6, or 35. If youre really getting into the debate and want to hash out (or defend) your answer, check out the entire Quora discussion for different users mathematical methodsand then check out these math puzzles for more brain busters. How to Solve the Infuriating Viral Math Problem, 10 of the Hardest Math Problems Ever Solved, Why No Humanoid Hobbits Are Still Living. See how you. Here we come with triangle puzzle image. How do you calculate that? 1. Triangle FGB is 6 square kilometers in size. So if you only counted one, or four, keep counting. In the artists signature, there is a hidden A.. Thank you for watching my blog friend, Counting triangles with in Square, Rectangle, Quadrilateral, Number of possible triangles within a triangle, How to Calculate Number of Triangles in a Square | Trick to Count no of Triangles, Triangle having number of bisects with vertex, Triangle having number of bisects with vertex and horizontal lines, Find the Number of triangles in the given figure | Count the number of triangles. (The caveat, evident in looking the diagram, is that no two lines are parallel, and there are no points where more than two lines intersect.) There is also a puzzle here where you will need to find the circles. Lenstore has put together a series of shape identification puzzles, and theyre anything but easyin fact, only 0.6% of people who took it got every question right. If youre into shapes, also try to figure out how many squares are in this image. Sponsored Links, A graphic shows a series of odd math equations and asks readers to fill in the final answer. Get a look at them all in this animation. But its only a matter of time before they discover itand argue some more. There is no definitive answer to this question as it depends on the specific characteristics of the triangles in question. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below.
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how many triangles puzzle answer 13 2023