tag:blogger.com,1999:blog-3802979373213475425.post626212832925773507..comments2019-04-20T15:33:02.879+05:30Comments on Critical Thinking Puzzles: Ant on a CubeUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3802979373213475425.post-53316019973170463212011-11-23T13:05:43.477+05:302011-11-23T13:05:43.477+05:30You have really done a great work to share the hid...You have really done a great work to share the hidden art of the great man. It is really a nice work by them. Thanks a lot for thisCaterpillar Turbohttp://www.turbochargerpros.com/turboparts/Caterpillar/All_Models/Turbocharger.htmlnoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-70042933416644057452011-11-08T16:52:16.331+05:302011-11-08T16:52:16.331+05:30Similarly for 2nd part. Here there will be 2 equat...Similarly for 2nd part. Here there will be 2 equations for b. <br /><br />b(a) is expected number of steps when ant is coming from a to b.<br /><br />b(c) is expected number of steps when ant is coming from c to b.<br /><br />a = 1+b(a)<br /><br />b(a) = 1+c<br /><br />c = 1+b(c)/2<br /><br />b(c) = 1+ a/2 + c/2<br /><br /><br />all equations are formulated on the same logic<br /><br />This returns a = 6Raghavhttps://www.blogger.com/profile/09186521256836841332noreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-26622005767846502512011-11-08T16:38:59.785+05:302011-11-08T16:38:59.785+05:30Lets say the expected number of steps for ant is a...Lets say the expected number of steps for ant is a<br /><br />expected number of steps from 3 corners immediately next to ant is b.<br /><br />and expected number of steps from 3 corners immediately next to sugar is c.<br /><br />If ant is at c, it chooses the path for sugar with probability 1/3 which takes (1+0) steps and with 2/3 probability for choosing two 'b' corners which now will take it (1+b) steps. <br />now c = (1/3)*(1+0)+(2/3)*(1+b) as these corners will have 2 b's next to them and one corner with sugar.<br />thus c = 1+(2/3)*b<br /><br />similarly b = (1/3)*(1+a)+(2/3)*(1+c)<br /><br />thus b = 1+(2/3)*c + (1/3)*a<br /><br />and similarly a = 1+b <br />as it is surrounded from all sides by 'b' corner.<br /><br />all these three equations gives expected number of steps for ant a=10.Raghavhttps://www.blogger.com/profile/09186521256836841332noreply@blogger.com