Your mission, should you choose to accept it, is to total up all of the triangles in this photo, including the triangles made up of other triangles. 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. Hint: Here having total two diagonals and having eight blocks. 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) How about 2,300 lines? This ones similar to this tricky triangle puzzle that stumped the internet a few years back. Count or Create The Crossword Solver finds answers to classic crosswords and cryptic crossword puzzles. Behold: That kind of dedication is just one of many reasons I love Popular Mechanics readers. In the how many triangles puzzle, there are a number of small triangles arranged in a larger triangle. It follows that the total number of triangles will be equal to the number of three-line combinations that can be chosen from a group of six lines. Impressively, this puzzles creators managed to squeeze eight different hexagons into one larger hexagon (which counts as one of the eight). There is also a puzzle here where you will need to find the circles. (function() { The first part n!/(nr)! .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. Math produces the solution and the rationale for it. In the problem by Dr. Loh, the calculation for the number of triangles can be rewritten like this: 6!/(3!3!). Just go by size. You can use the same procedure for multiple lines. Heres where math becomes powerful. The actual correct answer was Back at work, which the contestant guessed in underone minute. 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). These cookies will be stored in your browser only with your consent. Lets hear from reader Derek Schneider, who sent in another graphic suggesting there are 45 triangles.