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The problem in this video comes from a 1982 SAT exam this math problem was so hard that no one selected the correct answer can you figure it out in the following figure circle a has one-third the radius of circle B circle a rolls around circle B one trip back to its starting point how many times will Circle a revolved in total the answer choices are three halves three six nine halves and nine get out some pencil and paper and see if you can figure it out remember this was on the SAT, so it's a timed exam and the students would have had to figure it out just using pencil and paper here is what the test preparers thought when they made the question if circle a rolls around a distance of three times its circumference if you do it very carefully you'll find that circle a will roll around three times in total and that's what they thought the correct answer should be but let's do a little experiment and see what actually happens if we have circled a rolling around circle B I've made cardboard cutouts of these circles if circle a starts at the top and I carefully roll it around circle B after 14 of the distance circle a has already revolved around one time when we go halfway around circle B circle an around a second time as we continue around will see that by 34 of the distance circle a will roll a third time and when we complete the trip as circle a rolls around circle B when it completes the trip this will be a fourth time that circle a has rolled round, so the correct answer is four, and they actually made a mistake they did not include this as the correct answer they forgot to take into account that circle an is revolving around circle B and that would have added one more trip around lets try and solve this problem in general imagine having two coins of equal circumference you would think the answer might be one, but you see that when the coin rolls around halfway its already rolled around one time when it rolls around the remaining distance it will roll around a second time, so we can solve this problem and well see the correct answer is that circle a will roll around n plus 1 times the reason is that circle B has end times the circumference and that will account for n times that the circle a revolves around itself, but then we will also get one more revolution because circle an is also revolving around the center of circle B, so the correct answer is n plus 1 it's a pretty interesting problem I hope you liked the video please subscribe to my channel I make videos on math and game theory you can catch me on my blog mind your decisions which you can follow on Facebook Google and Patreon you can also catch me at brushed all occur on social media and if you like the video please check out my books I've provided links in the video description thanks for watching
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