1 00:00:07,310 --> 00:00:08,170 Hi everybody! 2 00:00:08,320 --> 00:00:12,390 My name is Jason Ermer and this is the first challenge video for the new blog 3 00:00:12,560 --> 00:00:15,030 that I’m experimenting with called Collaborative Mathematics. 4 00:00:16,160 --> 00:00:22,410 If you haven’t watched the How It Works video that explains the whole idea 5 00:00:22,560 --> 00:00:25,270 behind this blog, you might want to check that out. 6 00:00:25,670 --> 00:00:29,940 Since this is the first challenge video, I thought we would do a problem that 7 00:00:30,080 --> 00:00:31,260 was sort of an introduction. 8 00:00:31,470 --> 00:00:35,190 I’ll introduce myself to you by defining an Ermer Number. 9 00:00:35,400 --> 00:00:38,670 And we’ll explore some things about Ermer Numbers. 10 00:00:38,960 --> 00:00:43,040 An Ermer Number is a number that looks like my last name. 11 00:00:43,250 --> 00:00:46,130 More specifically, it’s a five digit number 12 00:00:46,310 --> 00:00:48,570 of the form e-r-m-e-r 13 00:00:48,750 --> 00:00:52,640 where e, r, and m are distinct digits. 14 00:00:54,240 --> 00:00:57,520 For example, the number 29,129 15 00:00:57,710 --> 00:00:59,440 twenty-nine thousand one hundred twenty-nine 16 00:00:59,810 --> 00:01:00,610 that’s an Ermer Number. 17 00:01:01,710 --> 00:01:04,460 40,740 is an Ermer Number. 18 00:01:05,320 --> 00:01:11,090 But the number 60,206 sixty thousand two hundred six 19 00:01:11,240 --> 00:01:12,100 that’s not an Ermer number. 20 00:01:12,720 --> 00:01:15,540 And 12,345 twelve thousand three hundred 21 00:01:15,680 --> 00:01:17,210 forty-five that’s not an Ermer Number either. 22 00:01:18,170 --> 00:01:22,410 So, having defined which numbers are Ermer Numbers and which are not, the 23 00:01:22,590 --> 00:01:24,600 core challenge this time is: 24 00:01:24,980 --> 00:01:29,340 How many Ermer Numbers are even? 25 00:01:30,220 --> 00:01:33,920 So if you can answer that question and explain your solution, then great! 26 00:01:34,130 --> 00:01:36,210 Go ahead and upload your response video! 27 00:01:36,530 --> 00:01:39,800 If you can answer the core challenge question, you might be interested in 28 00:01:39,930 --> 00:01:43,240 thinking about some other questions that come to mind. 29 00:01:43,790 --> 00:01:47,250 For example we’re talking about even Ermer Numbers. 30 00:01:47,450 --> 00:01:50,900 You might wonder how many Ermer Numbers are multiples of three. 31 00:01:51,370 --> 00:01:52,730 How many are multiples of 7? 32 00:01:53,070 --> 00:01:54,810 There’s all sorts of questions just like that. 33 00:01:55,080 --> 00:01:59,700 What’s the smallest distance between two consecutive Ermer Numbers? 34 00:02:00,990 --> 00:02:03,710 What’s the smallest difference between two consecutive Ermer Numbers? 35 00:02:03,900 --> 00:02:06,960 What’s the largest difference between twoconsecutive Ermer Numbers? 36 00:02:08,020 --> 00:02:12,470 Are there any Ermer Numbers that are prime? What sort of properties 37 00:02:12,660 --> 00:02:13,690 would they have? 38 00:02:14,630 --> 00:02:16,760 In addition to being prime, I mean. 39 00:02:16,970 --> 00:02:21,330 Anyway there’s a lot of questions that might come to mind. If you discover 40 00:02:21,480 --> 00:02:23,320 other interesting properties of Ermer numbers 41 00:02:23,550 --> 00:02:25,880 or if other questions come to mind -- whether or not 42 00:02:26,010 --> 00:02:28,040 you can answer them -- it’s cool if you just 43 00:02:28,200 --> 00:02:30,870 put those in your response video so that we can all think about them. 44 00:02:31,530 --> 00:02:36,320 Okay! There it is! Go have some fun and do some math! 45 00:02:36,540 --> 00:02:37,370 And check us out online. 46 00:02:37,780 --> 00:02:39,800 We’re at collaborative mathematics.org 47 00:02:40,020 --> 00:02:42,850 You can find us on Facebook and Google Plus. 48 00:02:43,190 --> 00:02:44,770 You can follow us on Twitter. 49 00:02:45,020 --> 00:02:46,490 You can subscribe to the YouTube channel. 50 00:02:46,830 --> 00:02:49,250 All those things might be things you want to do. 51 00:02:49,670 --> 00:02:53,160 Otherwise, I look forward to seeing what happens next!