title

Why this puzzle is impossible

description

Featuring quite a few science/math YouTubers!
Vihart response: https://youtu.be/CruQylWSfoU
Brought to you by you: http://3b1b.co/mug-thanks
And by Brilliant: https://brilliant.org/3b1b
Timestamps:
0:00 - Featured guests
4:30 - Why it's "impossible"
12:20 - Surfaces with holes
16:27 - Your challenge
17:35 - Sponsorship and end
Thanks to all the following channels for participating.
Standup Maths
https://www.youtube.com/user/standupmaths
Wendover Productions
https://www.youtube.com/user/Wendoverproductions
Welch Labs:
https://www.youtube.com/user/Taylorns34
MinutePhysics:
https://www.youtube.com/user/minutephysics
Ben Eater:
https://www.youtube.com/user/eaterbc
Mathologer:
https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg
Singing Banana:
https://www.youtube.com/user/singingbanana
Numberphile:
https://www.youtube.com/user/numberphile
Looking Glass Universe:
https://www.youtube.com/user/LookingGlassUniverse
Veritasium:
https://www.youtube.com/user/1veritasium
Steve Mould:
https://www.youtube.com/user/steventhebrave
Special thanks to MathsGear for providing the mugs.
https://mathsgear.co.uk/
https://mathsgear.co.uk/products/gift-card
Music:
Vincent Rubinetti: https://soundcloud.com/vincerubinetti/
Divertissement by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100256
Artist: http://incompetech.com/
------------------
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detail

{'title': 'Why this puzzle is impossible', 'heatmap': [{'end': 675.838, 'start': 655.028, 'weight': 1}, {'end': 918.807, 'start': 906.253, 'weight': 0.741}], 'summary': "Delves into challenging math and gas line puzzles, including attempts by youtubers to solve a math puzzle drawing non-crossing lines between utilities and houses, and connecting seven houses in a gas line puzzle using a dry erase marker on a mug. it discusses proving impossibility using planar graphs and euler's formula, analyzing the utilities puzzle, and solving topological and math puzzles on a mug within a timeframe, emphasizing topological properties.", 'chapters': [{'end': 297.963, 'segs': [{'end': 30.795, 'src': 'embed', 'start': 4.286, 'weight': 1, 'content': [{'end': 8.587, 'text': "It's the holiday season, a time of year to bring people together and to do something a little bit different.", 'start': 4.286, 'duration': 4.301}, {'end': 10.488, 'text': 'So Mathologer here.', 'start': 9.168, 'duration': 1.32}, {'end': 13.269, 'text': "I'm Matt Parker from Stand Up Maths.", 'start': 10.868, 'duration': 2.401}, {'end': 17.05, 'text': 'Hey, this is Sam from Wendover Productions and Half as Interesting.', 'start': 13.489, 'duration': 3.561}, {'end': 20.111, 'text': 'Hi everyone, this is James Grime from the Singing Banana channel.', 'start': 17.07, 'duration': 3.041}, {'end': 25.033, 'text': "It's Brady reporting for service from Numberphile, Objectivity and various other channels.", 'start': 20.351, 'duration': 4.682}, {'end': 27.154, 'text': 'Hey everyone, my name is Stephen Welch.', 'start': 25.053, 'duration': 2.101}, {'end': 28.634, 'text': 'My channel is Welch Labs.', 'start': 27.214, 'duration': 1.42}, {'end': 30.795, 'text': "I'm from the channel Looking Glass Universe.", 'start': 28.854, 'duration': 1.941}], 'summary': 'Math and science creators come together for the holiday season.', 'duration': 26.509, 'max_score': 4.286, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H04286.jpg'}, {'end': 88.651, 'src': 'embed', 'start': 47.114, 'weight': 0, 'content': [{'end': 50.895, 'text': "So I've been instructed not to read the directions before starting.", 'start': 47.114, 'duration': 3.781}, {'end': 51.635, 'text': 'Hi, Ben.', 'start': 51.315, 'duration': 0.32}, {'end': 52.456, 'text': 'Hi, Grant.', 'start': 52.116, 'duration': 0.34}, {'end': 54.296, 'text': 'So a friend just gave me this mug.', 'start': 52.936, 'duration': 1.36}, {'end': 55.736, 'text': 'You are going to be challenged.', 'start': 54.756, 'duration': 0.98}, {'end': 58.057, 'text': "I'm just going to kind of make you do this on camera to embarrass you.", 'start': 55.756, 'duration': 2.301}, {'end': 64.899, 'text': "We've got three different houses here, three different cottages, and then three different utilities, the gas, the power, and the water.", 'start': 58.857, 'duration': 6.042}, {'end': 69.62, 'text': 'Draw a line from each of the three utilities to each of the three houses, so nine lines in total.', 'start': 65.579, 'duration': 4.041}, {'end': 72.466, 'text': 'Okay, without letting any two cross.', 'start': 70.185, 'duration': 2.281}, {'end': 74.406, 'text': 'No two lines cross.', 'start': 73.086, 'duration': 1.32}, {'end': 81.589, 'text': "So right here, if you wanted to just go straight from power to the house, that's a no-go, right? Okay, interesting.", 'start': 74.907, 'duration': 6.682}, {'end': 82.889, 'text': 'That is quite the challenge.', 'start': 81.609, 'duration': 1.28}, {'end': 85.67, 'text': "So nine lines that don't cross.", 'start': 83.549, 'duration': 2.121}, {'end': 87.31, 'text': "That doesn't even sound possible.", 'start': 85.71, 'duration': 1.6}, {'end': 88.651, 'text': "I've got my mug.", 'start': 87.691, 'duration': 0.96}], 'summary': 'A challenge to connect 3 utilities to 3 houses with 9 non-crossing lines.', 'duration': 41.537, 'max_score': 47.114, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H047114.jpg'}, {'end': 297.963, 'src': 'embed', 'start': 236.238, 'weight': 3, 'content': [{'end': 238.12, 'text': 'We just need to figure out how to get that red in there.', 'start': 236.238, 'duration': 1.882}, {'end': 241.562, 'text': 'House number three is all done and good.', 'start': 239.181, 'duration': 2.381}, {'end': 242.303, 'text': 'Look at that.', 'start': 241.843, 'duration': 0.46}, {'end': 243.864, 'text': 'House number three, good to go.', 'start': 242.583, 'duration': 1.281}, {'end': 251.75, 'text': "So this house has all three and that house has all three, but this one in the middle doesn't have gas.", 'start': 244.404, 'duration': 7.346}, {'end': 254.112, 'text': 'All right, let me try something new.', 'start': 253.171, 'duration': 0.941}, {'end': 257.563, 'text': 'Let me just try and experiment here.', 'start': 256.06, 'duration': 1.503}, {'end': 260.286, 'text': "Let's be empirical.", 'start': 257.762, 'duration': 2.524}, {'end': 264.071, 'text': "What's really nice about the mug is that it's shiny.", 'start': 261.348, 'duration': 2.723}, {'end': 267.776, 'text': 'So if you use a dry erase marker, you can undo your mistakes.', 'start': 264.131, 'duration': 3.645}, {'end': 268.437, 'text': 'You just rub it off.', 'start': 267.796, 'duration': 0.641}, {'end': 275.579, 'text': "Posit! Okay so there's some very pleasing math within this puzzle for you and me to dive into,", 'start': 270.458, 'duration': 5.121}, {'end': 280.92, 'text': 'but first let me just say a really big thanks to everyone here who was willing to be my guinea pigs in this experiment.', 'start': 275.579, 'duration': 5.341}, {'end': 286.721, 'text': 'Each of them runs a channel that I respect a lot, and many of them have been incredibly kind and helpful to this channel.', 'start': 281.52, 'duration': 5.201}, {'end': 292.562, 'text': "So if there's any there that you're unfamiliar with or that you haven't been keeping track with, they're all listed in the description,", 'start': 287.201, 'duration': 5.361}, {'end': 294.142, 'text': 'so most certainly check them out.', 'start': 292.562, 'duration': 1.58}, {'end': 296.123, 'text': "We'll get back to all of them in just a minute.", 'start': 294.643, 'duration': 1.48}, {'end': 297.963, 'text': "Here's the thing about the puzzle.", 'start': 296.883, 'duration': 1.08}], 'summary': 'Experimenting with red in houses, dry erase marker removes mistakes, thanking guinea pigs for help.', 'duration': 61.725, 'max_score': 236.238, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0236238.jpg'}], 'start': 4.286, 'title': 'Challenging math and gas line puzzles', 'summary': 'Features youtubers attempting a math puzzle to draw non-crossing lines between utilities and houses, and solving a gas line puzzle by connecting seven houses while experimenting with a dry erase marker on a mug for better visualization and seeking inspiration from other channels.', 'chapters': [{'end': 109.391, 'start': 4.286, 'title': 'Math puzzle challenge', 'summary': 'Features a group of youtubers attempting a challenging math puzzle involving drawing nine non-crossing lines between three utilities and three houses, using a mug and markers, in a holiday collaboration video.', 'duration': 105.105, 'highlights': ['The challenge involves drawing nine non-crossing lines between three utilities and three houses, without any two lines crossing, creating a difficult math puzzle.', 'The YouTubers featured in the video include Matt Parker from Stand Up Maths, Sam from Wendover Productions, James Grime from the Singing Banana channel, Stephen Welch from Welch Labs, and Brady from Numberphile and Objectivity.', 'The participants express their willingness to take on the challenge, with some concerns about potential mistakes and difficulties in solving the puzzle.', 'The collaboration takes place during the holiday season, emphasizing the theme of bringing people together to engage in a unique and enjoyable activity.']}, {'end': 297.963, 'start': 109.411, 'title': 'Gas line puzzle exploration', 'summary': 'Involves solving a gas line puzzle involving connecting seven houses to a gas line, encountering challenges and making errors, eventually resorting to experimenting with a dry erase marker on a mug for better visualization and seeking inspiration from other channels.', 'duration': 188.552, 'highlights': ['The speaker attempts to solve a gas line puzzle involving connecting seven houses to a gas line, encountering challenges and making errors, eventually resorting to experimenting with a dry erase marker on a mug for better visualization.', 'The speaker expresses the need for gas to reach certain houses, with three houses successfully connected but encountering difficulty with the fourth house, demonstrating the quantifiable data of successfully connecting three houses.', 'The speaker expresses the need to seek inspiration from other channels and expresses gratitude towards individuals who have been helpful to the channel, emphasizing the importance of their support and encouraging the audience to explore the listed channels in the description.']}], 'duration': 293.677, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H04286.jpg', 'highlights': ['The challenge involves drawing nine non-crossing lines between three utilities and three houses, creating a difficult math puzzle.', 'The YouTubers featured include Matt Parker, Sam, James Grime, Stephen Welch, and Brady from various math and science channels.', 'The collaboration takes place during the holiday season, emphasizing the theme of bringing people together for a unique and enjoyable activity.', 'The speaker attempts to solve a gas line puzzle involving connecting seven houses, encountering challenges and making errors.', 'The speaker expresses the need for gas to reach certain houses, with three houses successfully connected, demonstrating quantifiable data.', 'The speaker resorts to experimenting with a dry erase marker on a mug for better visualization while solving the gas line puzzle.', 'The participants express their willingness to take on the challenge, with some concerns about potential mistakes and difficulties.', 'The speaker expresses the need to seek inspiration from other channels and gratitude towards helpful individuals.']}, {'end': 724.264, 'segs': [{'end': 377.022, 'src': 'embed', 'start': 337.553, 'weight': 0, 'content': [{'end': 338.774, 'text': 'What matters is the connections.', 'start': 337.553, 'duration': 1.221}, {'end': 343.056, 'text': "But in some peculiar cases, like this one, the thing that we care about is how it's drawn.", 'start': 339.194, 'duration': 3.862}, {'end': 348.339, 'text': "And if you can draw a graph in the plane without crossing its edges, it's called a planar graph.", 'start': 343.476, 'duration': 4.863}, {'end': 355.803, 'text': 'So the question before us is whether or not our utilities puzzle graph, which in the lingo is fancifully called a complete bipartite graph,', 'start': 349.059, 'duration': 6.744}, {'end': 357.604, 'text': 'K is planar or not.', 'start': 355.803, 'duration': 1.801}, {'end': 365.113, 'text': "And at this point, there are two kinds of viewers, those of you who know about Euler's formula and those who don't.", 'start': 360.629, 'duration': 4.484}, {'end': 367.715, 'text': 'Those who do might see where this is going.', 'start': 365.873, 'duration': 1.842}, {'end': 372.358, 'text': 'But rather than pulling out a formula from thin air and using it to solve the metapuzzle,', 'start': 368.075, 'duration': 4.283}, {'end': 377.022, 'text': 'I want to flip things around here and show how reasoning through this conundrum, step by step,', 'start': 372.358, 'duration': 4.664}], 'summary': 'Determining planarity of a complete bipartite graph for utilities puzzle.', 'duration': 39.469, 'max_score': 337.553, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0337553.jpg'}, {'end': 684.065, 'src': 'heatmap', 'start': 641.36, 'weight': 4, 'content': [{'end': 648.742, 'text': 'So any graph that cuts the plane into 5 regions, where each region is touching 4 edges, would have to have 10 total edges.', 'start': 641.36, 'duration': 7.382}, {'end': 653.667, 'text': 'But our utilities puzzle has only nine edges available.', 'start': 650.745, 'duration': 2.922}, {'end': 660.471, 'text': 'So even though we concluded that it would have to cut the plane into five regions, it would be impossible for it to do that.', 'start': 655.028, 'duration': 5.443}, {'end': 661.732, 'text': 'So there you go.', 'start': 661.212, 'duration': 0.52}, {'end': 662.713, 'text': 'Bada boom, bada bang.', 'start': 661.852, 'duration': 0.861}, {'end': 666.896, 'text': 'It is impossible to solve this puzzle on a piece of paper without intersecting lines.', 'start': 662.793, 'duration': 4.103}, {'end': 668.617, 'text': "Tell me that's not a slick proof.", 'start': 667.496, 'duration': 1.121}, {'end': 675.838, 'text': "And before getting back to our friends and the mug, it's worth taking a moment to pull out a general truth sitting inside of this.", 'start': 670.154, 'duration': 5.684}, {'end': 684.065, 'text': 'Think back to the key rule where each new edge was introducing either a new vertex by being drawn to an untouched spot,', 'start': 676.539, 'duration': 7.526}], 'summary': 'A graph with 10 edges needed to cut plane into 5 regions, but 9 edges make it impossible. slick proof of impossibility.', 'duration': 42.705, 'max_score': 641.36, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0641360.jpg'}, {'end': 736.606, 'src': 'embed', 'start': 708.296, 'weight': 1, 'content': [{'end': 712.94, 'text': "And this relation, true for any planar graph, is called Euler's characteristic formula.", 'start': 708.296, 'duration': 4.644}, {'end': 719.503, 'text': 'Historically, by the way, the formula came up in the context of convex polyhedra, like a cube, for example,', 'start': 714.042, 'duration': 5.461}, {'end': 724.264, 'text': 'where the number of vertices minus the number of edges plus the number of faces always equals two.', 'start': 719.503, 'duration': 4.761}, {'end': 729.305, 'text': 'So when you see it written down, you often see it with an F for faces instead of talking about regions.', 'start': 724.944, 'duration': 4.361}, {'end': 736.606, 'text': 'Now, before you go thinking of me as some kind of Grinch that sends friends an impossible puzzle and then makes them film themselves trying to solve it.', 'start': 730.605, 'duration': 6.001}], 'summary': "Euler's characteristic formula applies to planar graphs, where v - e + f always equals 2.", 'duration': 28.31, 'max_score': 708.296, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0708296.jpg'}], 'start': 298.503, 'title': "Planar graphs and euler's formula", 'summary': "Discusses proving impossibility using planar graphs and euler's formula, analyzing the utilities puzzle and its relation to euler's characteristic formula, providing insights into these concepts.", 'chapters': [{'end': 377.022, 'start': 298.503, 'title': 'Proving the impossible', 'summary': "Discusses the approach of proving the impossibility of a task by exploring the concept of planar graphs and the challenge of determining whether a specific graph is planar or not, highlighting the relevance of euler's formula in this context.", 'duration': 78.519, 'highlights': ['The concept of planar graphs and the challenge of determining whether a specific graph is planar or not are discussed, with a specific focus on the utilities puzzle graph, known as a complete bipartite graph, K.', "The relevance and application of Euler's formula in solving the metapuzzle and determining the planarity of a graph is emphasized, highlighting the two kinds of viewers - those familiar with Euler's formula and those who are not.", 'The discussion emphasizes the importance of reasoning through the conundrum step by step rather than relying solely on pulling out a formula to solve the metapuzzle.']}, {'end': 724.264, 'start': 377.022, 'title': "Utilities puzzle and euler's characteristic", 'summary': "Delves into analyzing the utilities puzzle, revealing that a hypothetical solution would cut the plane into five separate regions, but it would be impossible due to the number of edges available. this insight leads to euler's characteristic formula, applicable to any planar graph.", 'duration': 347.242, 'highlights': ['A hypothetical solution to the utilities puzzle would cut the plane into five separate regions, but it would be impossible due to the number of available edges.', "Euler's characteristic formula states that the number of vertices minus the number of edges plus the number of regions remains unchanged for any planar graph, starting at 2 and always staying at 2.", "The number of vertices minus the number of edges plus the number of regions remains unchanged, a concept known as Euler's characteristic formula."]}], 'duration': 425.761, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0298503.jpg', 'highlights': ['The concept of planar graphs and determining graph planarity is discussed, focusing on the utilities puzzle graph, K.', "Euler's formula's relevance in solving the metapuzzle and determining graph planarity is emphasized.", 'The importance of reasoning through the conundrum step by step is highlighted.', "Euler's characteristic formula states the number of vertices minus edges plus regions remains unchanged for any planar graph.", 'A hypothetical solution to the utilities puzzle would cut the plane into five separate regions, but it would be impossible.']}, {'end': 1174.819, 'segs': [{'end': 792.974, 'src': 'embed', 'start': 765.768, 'weight': 1, 'content': [{'end': 774.071, 'text': "I'm gonna start by, um, I think taking advantage of the handle because I think that that is the key to this.", 'start': 765.768, 'duration': 8.303}, {'end': 778.933, 'text': 'You know what? I think actually a sphere is the wrong thing to be thinking about.', 'start': 774.412, 'duration': 4.521}, {'end': 785.036, 'text': 'I mean, like, famously a mug is topologically the same as a donut.', 'start': 778.953, 'duration': 6.083}, {'end': 790.734, 'text': "So to solve this thing, you're going to have to use the Taurusiness of the mug.", 'start': 785.512, 'duration': 5.222}, {'end': 792.974, 'text': "You're going to have to use the handle somehow.", 'start': 790.754, 'duration': 2.22}], 'summary': 'Utilize the handle and topology of a mug to solve the problem.', 'duration': 27.206, 'max_score': 765.768, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0765768.jpg'}, {'end': 920.829, 'src': 'heatmap', 'start': 886.883, 'weight': 0, 'content': [{'end': 889.704, 'text': 'In through the front door, out through the back door, done.', 'start': 886.883, 'duration': 2.821}, {'end': 891.445, 'text': 'No intersections.', 'start': 890.685, 'duration': 0.76}, {'end': 893.807, 'text': "Maybe you think that's cheating.", 'start': 892.566, 'duration': 1.241}, {'end': 899.249, 'text': "Well, it's a topological puzzle, so it means the relative positions of things don't matter.", 'start': 894.087, 'duration': 5.162}, {'end': 904.272, 'text': 'What that means is we can take this handle and move it here, creating another connection.', 'start': 899.389, 'duration': 4.883}, {'end': 905.533, 'text': 'Ho, ho, ho.', 'start': 904.772, 'duration': 0.761}, {'end': 912.896, 'text': 'Oh my god, am I done? Is this over? I think I might have gotten it.', 'start': 906.253, 'duration': 6.643}, {'end': 913.357, 'text': '24 minutes.', 'start': 912.916, 'duration': 0.441}, {'end': 915.498, 'text': 'Grant, you said this would take 15 minutes.', 'start': 913.997, 'duration': 1.501}, {'end': 917.386, 'text': 'There you go.', 'start': 916.906, 'duration': 0.48}, {'end': 918.807, 'text': "I think I've solved it.", 'start': 917.406, 'duration': 1.401}, {'end': 920.829, 'text': "You're in the success category.", 'start': 919.608, 'duration': 1.221}], 'summary': 'Solved topological puzzle in 24 minutes, exceeding estimated 15 minutes.', 'duration': 33.946, 'max_score': 886.883, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0886883.jpg'}, {'end': 1011.576, 'src': 'embed', 'start': 975.564, 'weight': 3, 'content': [{'end': 979.507, 'text': 'Given just how helpful these three guys were in the logistics of a lot of this.', 'start': 975.564, 'duration': 3.943}, {'end': 985.572, 'text': 'really the least I could do to thank them is give a small plug for how gift cards from MathsGear could make a pretty good last minute Christmas present.', 'start': 979.507, 'duration': 6.065}, {'end': 990.42, 'text': 'Back to the puzzle though, this is one of those things where once you see it, it kind of feels obvious.', 'start': 986.397, 'duration': 4.023}, {'end': 994.743, 'text': 'The handle of the mug can basically be used as a bridge to prevent two lines from crossing.', 'start': 990.78, 'duration': 3.963}, {'end': 998.165, 'text': 'But this raises a really interesting mathematical question.', 'start': 995.543, 'duration': 2.622}, {'end': 1002.408, 'text': 'We just proved that this task is impossible for graphs on a plane.', 'start': 998.825, 'duration': 3.583}, {'end': 1009.515, 'text': "So where exactly does that proof break down on the surface of a mug? And I'm actually not going to tell you the answer here.", 'start': 1003.028, 'duration': 6.487}, {'end': 1011.576, 'text': 'I want you to think about this on your own.', 'start': 1009.895, 'duration': 1.681}], 'summary': 'Three guys helped with logistics; promoting mathsgear gift cards for christmas; discussing a math puzzle regarding the handle of a mug as a bridge for lines and a question about proof breakdown.', 'duration': 36.012, 'max_score': 975.564, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0975564.jpg'}, {'end': 1086.409, 'src': 'embed', 'start': 1054.062, 'weight': 4, 'content': [{'end': 1055.822, 'text': 'But, Grant, I hear you complaining.', 'start': 1054.062, 'duration': 1.76}, {'end': 1061.343, 'text': "how am I supposed to practice my problem solving if I don't have someone shipping me puzzles on topologically interesting shapes?", 'start': 1055.822, 'duration': 5.521}, {'end': 1067.785, 'text': "Well, let's close things off by going through a couple puzzles created by this week's mathematically oriented sponsor, Brilliant.org.", 'start': 1061.824, 'duration': 5.961}, {'end': 1073.066, 'text': "So here I'm in their Intro to Problem Solving course and going through a particular sequence called Flipping Pairs.", 'start': 1068.445, 'duration': 4.621}, {'end': 1078.607, 'text': "And the rules here seem to be that we can flip adjacent pairs of coins, but we can't flip them one at a time.", 'start': 1073.766, 'duration': 4.841}, {'end': 1086.409, 'text': 'And we are asked, is it possible to get it so that all three coins are gold side up? Well, clearly I just did it, so yes.', 'start': 1079.207, 'duration': 7.202}], 'summary': 'Introduction to problem solving with brilliant.org, solving a sequence called flipping pairs to get all three coins gold side up.', 'duration': 32.347, 'max_score': 1054.062, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H01054062.jpg'}], 'start': 724.944, 'title': 'Solving topological and math puzzles on a mug', 'summary': "Covers solving a topological puzzle involving a mug handle within 24 minutes despite a 15-minute timeframe, emphasizing topological properties. it also delves into a math puzzle on a mug, discussing crossing lines, impossibility of tasks on a plane, and a call to action for the sponsor's puzzles on a website run by three youtubers.", 'chapters': [{'end': 934.023, 'start': 724.944, 'title': 'Topological puzzle: mug handle solution', 'summary': 'Discusses solving a topological puzzle involving a mug handle, with the speaker successfully solving it in 24 minutes, despite an estimated 15-minute timeframe, emphasizing the use of the handle and topological properties of a mug.', 'duration': 209.079, 'highlights': ['The speaker successfully solves the puzzle in 24 minutes, exceeding the estimated 15-minute timeframe.', 'Emphasizing the use of the mug handle and its topological properties in solving the puzzle.', "Demonstrating a non-traditional approach to problem-solving by utilizing the handle's properties to navigate the puzzle's constraints."]}, {'end': 1174.819, 'start': 934.043, 'title': 'Math puzzle on a mug', 'summary': "Discusses a math puzzle involving a mug and a pen, the concept of crossing lines, the impossibility of certain tasks on a plane, and a math-oriented sponsor's puzzles, with a mention of a website run by three youtubers and a call to action to try the puzzles on the sponsor's platform.", 'duration': 240.776, 'highlights': ['The mug is used to prevent two lines from crossing, raising a mathematical question about the impossibility of certain tasks on a plane.', 'A mention of a website run by three YouTubers, with a call to action for gift cards from the website as a last-minute Christmas present.', "An introduction to math puzzles sponsored by Brilliant.org, with an example of a puzzle and a call to action to try the sponsor's puzzles."]}], 'duration': 449.875, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/VvCytJvd4H0/pics/VvCytJvd4H0724944.jpg', 'highlights': ['The speaker successfully solves the puzzle in 24 minutes, exceeding the estimated 15-minute timeframe.', 'Emphasizing the use of the mug handle and its topological properties in solving the puzzle.', "Demonstrating a non-traditional approach to problem-solving by utilizing the handle's properties to navigate the puzzle's constraints.", 'The mug is used to prevent two lines from crossing, raising a mathematical question about the impossibility of certain tasks on a plane.', "An introduction to math puzzles sponsored by Brilliant.org, with an example of a puzzle and a call to action to try the sponsor's puzzles.", 'A mention of a website run by three YouTubers, with a call to action for gift cards from the website as a last-minute Christmas present.']}], 'highlights': ['The speaker successfully solves the puzzle in 24 minutes, exceeding the estimated 15-minute timeframe.', 'The challenge involves drawing nine non-crossing lines between three utilities and three houses, creating a difficult math puzzle.', 'The concept of planar graphs and determining graph planarity is discussed, focusing on the utilities puzzle graph, K.', 'The YouTubers featured include Matt Parker, Sam, James Grime, Stephen Welch, and Brady from various math and science channels.', 'The speaker attempts to solve a gas line puzzle involving connecting seven houses, encountering challenges and making errors.', 'The collaboration takes place during the holiday season, emphasizing the theme of bringing people together for a unique and enjoyable activity.', 'The speaker expresses the need for gas to reach certain houses, with three houses successfully connected, demonstrating quantifiable data.', 'The speaker resorts to experimenting with a dry erase marker on a mug for better visualization while solving the gas line puzzle.', 'Emphasizing the use of the mug handle and its topological properties in solving the puzzle.', "Demonstrating a non-traditional approach to problem-solving by utilizing the handle's properties to navigate the puzzle's constraints."]}