1 00:00:04,220 --> 00:00:05,070 Hi everybody! 2 00:00:05,270 --> 00:00:07,620 It’s Jason again and this is Challenge #4 from 3 00:00:07,750 --> 00:00:08,940 Collaborative Mathematics. 4 00:00:09,840 --> 00:00:14,450 For this challenge, I’d like you to picture a very special calculator that has only 5 00:00:14,720 --> 00:00:23,880 two keys on it. It’s got the [+1] key and the [x3] key, and when you press either 6 00:00:24,010 --> 00:00:28,210 of these keys, they immediately do whatever they say they do. 7 00:00:28,420 --> 00:00:34,140 So if you image, for example, that the display screen on the calculator reads 8 00:00:34,330 --> 00:00:38,010 the number 20, and you hit the [+1] key, 9 00:00:38,210 --> 00:00:42,030 then the display immediately updates and shows the number 21. 10 00:00:42,460 --> 00:00:48,060 And if you then press the [x3] key, the calculator would immediately 11 00:00:48,240 --> 00:00:50,480 update and show the number 63. 12 00:00:50,650 --> 00:00:52,880 And here’s the challenge, using this calculator. 13 00:00:53,170 --> 00:00:57,370 Let’s assume that it starts with the number 0 on its display screen. 14 00:00:57,680 --> 00:01:03,130 The goal is to get the calculator to show the number 300 on the screen. 15 00:01:03,480 --> 00:01:05,390 And the challenge is: of button-presses that it takes to make 16 00:01:05,880 --> 00:01:13,080 What’s the smallest number of button- presses that it takes to make that happen? 17 00:01:13,490 --> 00:01:16,170 What’s the smallest number of button-presses to get this particular 18 00:01:16,350 --> 00:01:20,810 two-button calculator to go from 0 to 300? 19 00:01:21,690 --> 00:01:26,880 Remember here that one of the parts of this challenge is the “smallest number of 20 00:01:27,110 --> 00:01:30,710 button presses”. Right? If you can get from 0 to 300, that’s great! 21 00:01:31,100 --> 00:01:34,710 But be thinking about whether you’ve got the 22 00:01:34,900 --> 00:01:37,910 smallest number of button-presses to get there. 23 00:01:38,470 --> 00:01:41,980 And if you think you have the smallest number, if you think you’ve found the 24 00:01:42,110 --> 00:01:49,370 minimum, how do you know? Why do you think you can’t get from 0 to 300 with 25 00:01:49,530 --> 00:01:53,180 fewer button-presses than whatever solution you’ve found? 26 00:01:53,540 --> 00:01:56,680 So that’s it! That’s the challenge for this video, Challenge #4. 27 00:01:56,930 --> 00:02:00,060 I’ll invite you to check us out online, as usual. We’re at 28 00:02:00,200 --> 00:02:02,290 collaborative mathematics . org 29 00:02:02,710 --> 00:02:06,820 and from there you can find links to all of our social media, and you can access the 30 00:02:06,950 --> 00:02:11,560 archives which have links to all of the past Challenge Videos and the Video 31 00:02:11,730 --> 00:02:15,650 Responses that people have submitted. There’s quite a lot of cool stuff there, so 32 00:02:15,820 --> 00:02:17,390 I’ll encourage you to check that out! 33 00:02:17,790 --> 00:02:19,310 I look forward to seeing what happens next! 34 00:02:19,500 --> 00:02:19,910 Have fun!