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wu :: forums    riddles    easy (Moderators: SMQ, Icarus, Eigenray, ThudnBlunder, william wu, Grimbal, towr)    Buses « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Buses  (Read 550 times) Nootch Newbie     Posts: 16 Buses   « on: Sep 8th, 2004, 11:53am » Quote Modify On route 71X buses start from the Green Man at Ilworth and ply backwards and forwards between hostlry and the Shabby Tiger at Plugstead.   There are 11 buses on this route; each, on arriving at either terminus, waits for one minute and then begins the return journey.   Mr. Brightly, a bus driver from the provinces, boarded a bus at Green Man that other day and road all the way to Shabby Tiger, making a note every time he passed a 71X bus.  He passed on (so he calculated) every 1,320 yards, and estimated their average speed at 15 m.p.h   How many buses did he pass en route?   IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Buses   « Reply #1 on: Sep 8th, 2004, 4:08pm » Quote Modify Ouch!  Can you convert that into metric?  Kilometers and kilometers per hour?   Would make life easier for us Europeans. IP Logged asterix Guest Re: Buses   « Reply #2 on: Sep 8th, 2004, 8:09pm » Quote Modify Remove Not really. IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Buses   « Reply #3 on: Sep 8th, 2004, 11:59pm » Quote Modify on Sep 8th, 2004, 4:08pm, Grimbal wrote: Ouch!  Can you convert that into metric?  Kilometers and kilometers per hour?   Would make life easier for us Europeans.   ...even for French-speaking Europeans who prefer Americanized spelling?     « Last Edit: Sep 9th, 2004, 7:48am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Patashu Newbie     Gender: Posts: 18 Re: Buses   « Reply #4 on: Sep 9th, 2004, 4:39am » Quote Modify Ow. Yards make my brain hurt. Owie.   How long is a yard anyway? IP Logged John_Gaughan Uberpuzzler Behold, the power of cheese!     Gender: Posts: 767 Re: Buses   « Reply #5 on: Sep 9th, 2004, 6:42am » Quote Modify He passed 10 buses. IP Logged x = (0x2B | ~0x2B) x == the_question ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Buses   « Reply #6 on: Sep 9th, 2004, 7:55am » Quote Modify Quote: ...boarded a bus at Green Man that other day and road all the way to Shabby Tiger, making a note every time he passed a 71X bus. on Sep 9th, 2004, 6:42am, John_Gaughan wrote: He passed <hidden> buses. But he travelled only half the route. Were all 10 coming the other way?   « Last Edit: Sep 9th, 2004, 8:02am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. John_Gaughan Uberpuzzler Behold, the power of cheese!     Gender: Posts: 767 Re: Buses   « Reply #7 on: Sep 9th, 2004, 8:50am » Quote Modify No, but that is irrelevant. Start at the beginning. As he leaves, the bus directly behind him arrives next. They pass just a few minutes into the journey. A few minutes later he passes the bus two behind him, and so on. The last bus he passes right before pulling into the destination is the one in front of him, which departs right before he arrives.   Imagine a rubber band stretched between two small pulleys. There are eleven tick marks evenly spaced along the rubber band. As the pulleys turn, moving the band, each tick mark must pass each other mark once per half-revolution. IP Logged x = (0x2B | ~0x2B) x == the_question John_Gaughan Uberpuzzler Behold, the power of cheese!     Gender: Posts: 767 Re: Buses   « Reply #8 on: Sep 9th, 2004, 8:55am » Quote Modify on Sep 9th, 2004, 7:55am, THUDandBLUNDER wrote: But he travelled only half the route. Were all 10 coming the other way? Sorry, I did not quite address your question. Yes, all ten were coming the other way, at some point during his journey, but not necessarily the entire time. It only takes a second or two to pass, remember.   Think of a unit circle. Pick eleven unique half-circles. Assume one, our bus driver, is on the half-circle that starts at -1 and goes up to 1. Every other half-circle must have a portion that is decreasing. They cannot be strictly non-decreasing. So at some point on the arc, they are "coming the other way." IP Logged x = (0x2B | ~0x2B) x == the_question ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Buses   « Reply #9 on: Sep 9th, 2004, 9:37am » Quote Modify Yes, John, you are right.   « Last Edit: Sep 9th, 2004, 10:38am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Buses   « Reply #10 on: Sep 9th, 2004, 11:21am » Quote Modify on Sep 8th, 2004, 8:09pm, asterix wrote: Not really.   That's why I put the 2 smileys... 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