tag:blogger.com,1999:blog-3802979373213475425.post7631797716398255011..comments2024-03-17T20:25:54.267+05:30Comments on Critical Thinking Puzzles: Flight path puzzleAnonymoushttp://www.blogger.com/profile/05634752405801576739noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3802979373213475425.post-10137512470666461202010-03-12T00:11:18.064+05:302010-03-12T00:11:18.064+05:30yep ... its brillyep ... its brillSAKTHIhttps://www.blogger.com/profile/08451659375331466594noreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-56817670381232895932009-06-21T15:51:09.597+05:302009-06-21T15:51:09.597+05:30@danvdias
Yup, you're right. Ending on City 8...@danvdias<br /><br />Yup, you're right. Ending on City 8 caused me to forget that there was a City 9.<br /><br />Nice one.Secret Squïrrelnoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-34803964876632434962009-06-17T00:52:07.867+05:302009-06-17T00:52:07.867+05:30The question is: "From how many cities a flig...The question is: "From how many cities a flight can start"<br /><br />I mean the answer is: 8 cities (1, 2, 3, 4, 5, 6, 7 and 9... you can easily discover a route starting on all of them)<br /><br />About how many routes, in the answer above all routes with city "9" are missing, and another three ones.<br /><br />two-cities: (3)<br />1-8<br />4-8<br />7-8<br /><br />three-cities: (10 * 2! = 20)<br />1-3-8<br />1-6-8<br />1-9-8*<br />2-5-8<br />3-4-8<br />3-7-8<br />4-6-8<br />4-9-8*<br />6-7-8<br />7-9-8*<br /><br />four-cities: (15 * 3! = 90)<br />1-2-4-8<br />1-2-7-8<br />1-3-6-8<br />1-3-9-8*<br />1-4-5-8<br />1-5-7-8**<br />1-6-9-8*<br />2-3-5-8<br />2-4-7-8<br />2-5-6-8**<br />2-5-9-8*<br />3-4-6-8<br />3-4-9-8*<br />4-5-7-8<br />4-6-9-8*<br /><br />five-cities: (22 * 4! = 528)<br />1-2-3-4-8<br />1-2-3-7-8<br />1-2-4-6-8<br />1-2-4-9-8*<br />1-2-6-7-8**<br />1-2-7-9-8*<br />1-3-4-5-8<br />1-3-5-7-8<br />1-3-6-9-8*<br />1-4-5-6-8<br />1-4-5-9-8*<br />1-5-6-7-8<br />1-5-7-9-8*<br />2-3-4-7-8<br />2-3-5-6-8<br />2-3-5-9-8*<br />2-4-6-7-8<br />2-4-7-9-8*<br />3-4-5-7-8<br />3-4-6-9-8*<br />4-5-6-7-8<br />4-5-7-9-8*<br /><br />six-cities: (20 * 5! = 2400)<br />1-2-3-4-6-8<br />1-2-3-4-9-8*<br />1-2-3-6-7-8<br />1-2-3-7-9-8*<br />1-2-4-5-7-8<br />1-2-4-6-9-8*<br />1-2-6-7-9-8*<br />1-3-4-5-6-8<br />1-3-4-5-9-8*<br />1-3-5-6-7-8<br />1-3-5-7-9-8*<br />1-4-5-6-9-8*<br />1-5-6-7-9-8*<br />2-3-4-6-7-8<br />2-3-4-7-9-8*<br />2-3-5-6-9-8*<br />2-4-6-7-9-8*<br />3-4-5-6-7-8<br />3-4-5-7-9-8*<br />4-5-6-7-9-8*<br /><br />seven-cities: (9 * 6! = 6480)<br />1-2-3-4-5-7-8<br />1-2-3-4-6-9-8*<br />1-2-3-6-7-9-8*<br />1-2-4-5-6-7-8<br />1-2-4-5-7-9-8*<br />1-3-4-5-6-9-8*<br />1-3-5-6-7-9-8*<br />2-3-4-6-7-9-8*<br />3-4-5-6-7-9-8*<br /><br />eight-cities: (3 * 7! = 15120)<br />1-2-3-4-5-6-7-8<br />1-2-3-4-5-7-9-8*<br />1-2-4-5-6-7-9-8*<br /><br />nine-cities: (1 * 8! = 40320)<br />1-2-3-4-5-6-7-9-8*<br /><br />TOTAL = 64961danvdiasnoreply@blogger.comtag:blogger.com,1999:blog-3802979373213475425.post-3880354985362686122009-05-19T10:47:00.000+05:302009-05-19T10:47:00.000+05:30Assuming that you can't visit any city more than o...Assuming that you can't visit any city more than once and that I haven't missed any journeys the answer is 7673.<br /><br />This consists of the journeys listed below. Only pathways where successive cities having a higher number are listed but these cities can obviously be visited in any order as long as City 8 is the last; eg from the four-city group the path 1-2-4-8 represents these trips also: 1-4-2-8, 2-1-4-8, 2-4-1-8, 4-1-2-8, and 4-2-1-8 meaning that, for the four-city group, the number of paths listed must be multiplied by 6 to give the actual total.<br /><br />3 two-city trips (total=3)<br />1-8<br />4-8<br />7-8<br /><br />7 three-city trips, each of which can be travelled 2*1=2 ways (total=7*2=14)<br />1-3-8<br />1-6-8<br />2-5-8<br />3-4-8<br />3-7-8<br />4-6-8<br />6-7-8<br /><br />8 four-city trips, each of which can be travelled 3*2*1=6 ways (total=8*6=48)<br />1-2-4-8<br />1-2-7-8<br />1-3-6-8<br />1-4-5-8<br />2-3-5-8<br />2-4-7-8<br />3-4-6-8<br />4-5-7-8<br /><br />12 five-city trips, each of which can be travelled 4*3*2*1=24 ways (total=12*24=288)<br />1-2-3-4-8<br />1-2-3-7-8<br />1-2-4-6-8<br />1-3-4-5-8<br />1-3-5-7-8<br />1-4-5-6-8<br />1-5-6-7-8<br />2-3-4-7-8<br />2-3-5-6-8<br />2-4-6-7-8<br />3-4-5-7-8<br />4-5-6-7-8<br /><br />7 six-city trips, each of which can be travelled 5*4*3*2*1=120 ways (total=7*120=840)<br />1-2-3-4-6-8<br />1-2-3-6-7-8<br />1-2-4-5-7-8<br />1-3-4-5-6-8<br />1-3-5-6-7-8<br />2-3-4-6-7-8<br />3-4-5-6-7-8<br /><br />2 seven-city trips, each of which can be travelled 6*5*4*3*2*1=720 ways (total=2*720=1440)<br />1-2-3-4-5-7-8<br />1-2-4-5-6-7-8<br /><br />1 eight-city trip, each of which can be travelled 7*6*5*4*3*2*1=5040 ways (total=1*5040=5040)<br />1-2-3-4-5-6-7-8Secret Squïrrelnoreply@blogger.com