bonanova Posted January 23, 2009 Report Share Posted January 23, 2009 There's a spider lurking on the floor in the corner of a room. A fly comes to rest on the diagonally opposite corner of the floor and falls asleep. The spider sets out for the fly; but for his own safety, he does not walk on the floor. If the room is 40' x 56' with an 8' ceiling, how far must the spider walk for his lunch? What if the floor is only 4' x 6'? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 ~85 feet (up the wall, diagonally across the ceiling, and back down. shorter than going around the room on the wall, which would be 96 feet) If the floor is 4x6, then 10 feet (around the room on the wall) since going across the ceiling would be ~23 feet Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 Can not see that far, despite all those eyes - the food must come to him Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 I got ~86' but math in the head is dangerous at best. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 Can't the spider just walk along the wall, around the edge of the room, staying as close to the floor as possible. If this is true, then the spider would only walk 40+56 = 96 feet. However, if the spider goes up and over, then using pythagorean's theorem, the diagonal of the room is approximately 68.82 feet. So add 16 for the trip up to the ceiling and back down. Meaning the spider walks ~84.82 feet, which is a bit shorter than the other way.. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 23, 2009 Author Report Share Posted January 23, 2009 Can not see that far, despite all those eyes - the food must come to him I told the spider about the fly. It's a geometry problem: how far must the spider ... , not how far did the spider ... <_< Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 23, 2009 Author Report Share Posted January 23, 2009 Forgot to add - the spider has a range of only 82' then he dies of hunger. Does he survive? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 Forgot to add - the spider has a range of only 82' then he dies of hunger. Does he survive? In the smaller room easy, just walks around the walls. In the bigger room goes up and across the ceiling diagonal then lets go in the corner above the fly and gravity does the rest Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 Forgot to add - the spider has a range of only 82' then he dies of hunger. Does he survive? If the spider is particularly clever, he can make it in 79.2 feet by going diagonally up the wall at a 45-degree angle, crossing the ceiling at a 45-degree angle, and coming down the opposite wall at a 45-degree angle. If his range is only 82 feet, it's gonna be close. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 Forgot to add - the spider has a range of only 82' then he dies of hunger. Does he survive? Well, if the spider travels at almost the speed of light, then the fly... spider... um... -- ah, forget it. Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted January 23, 2009 Report Share Posted January 23, 2009 79.2' 562+(8+40+8)2=79.22 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 80 feet for the big one and 10 for the small one. square root of ((40+8)squared + (56+8) squared). Use the pythagorean theorem by adding the walls to the equation. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 There's a spider lurking on the floor in the corner of a room. A fly comes to rest on the diagonally opposite corner of the floor and falls asleep. The spider sets out for the fly; but for his own safety, he does not walk on the floor. If the room is 40' x 56' with an 8' ceiling, how far must the spider walk for his lunch? What if the floor is only 4' x 6'? 80.31624 feet Travels diagonally from the bottom left of the wall, to the top of the wall 8' in (8x8 square) [11.31371 feet] Travels diagonally from 8' into the beginning wall to 8' from the destination wall (32x48 square) [57.68882 feet]. Travels diagonally from 8' from the wall to the corner and eats the fly [11.31371 feet]. If the floor were 4' x 6' the spider would only have to travel 10': Just around the wall. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 The decent isn't counted in "distance walked" right? Because once he is directly over the fly he can just drop down without walking. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 The spider will not die of hunger if he goes to the right spots on the walls. As long as I didn't fat finger something in the coding. He has many possibilities to make it there before 82. 6 11 80.00182512 6 10 80.00764706 6 12 80.0279602 7 11 80.03484203 5 10 80.04161367 5 11 80.0442229 7 10 80.04911371 6 9 80.05021463 7 12 80.05235091 5 9 80.07591701 5 12 80.07895742 6 13 80.08221782 7 13 80.09780427 7 9 80.09995645 8 11 80.13292978 6 8 80.13547318 8 12 80.14179564 5 13 80.14198376 5 8 80.15307659 8 10 80.15565988 6 14 80.16153984 4 10 80.16284785 7 14 80.16814275 4 11 80.17386056 8 13 80.17841915 4 9 80.18890695 7 8 80.19331783 8 9 80.21477898 4 12 80.21715863 5 14 80.23024436 8 14 80.23973913 4 8 80.25798041 7 15 80.26093528 6 15 80.26349594 6 7 80.27073602 5 7 80.28040381 9 11 80.28736946 9 12 80.28758624 4 13 80.288909 9 13 80.31536522 8 8 80.31623741 9 10 80.31855605 8 15 80.32332299 7 7 80.33651358 5 15 80.34130902 9 14 80.36764262 7 16 80.37425828 4 7 80.37737818 3 10 80.38414079 9 9 80.3859422 4 14 80.38605415 6 16 80.38616281 3 9 80.40198404 3 11 80.40352091 8 16 80.42724622 9 15 80.44198368 3 12 80.45533825 3 8 80.46299254 6 6 80.46486583 5 6 80.46675921 8 7 80.46735387 5 16 80.47325402 10 12 80.4825614 10 11 80.49098812 9 8 80.49548159 10 13 80.50149291 4 15 80.50616337 7 17 80.50659914 6 17 80.52802751 10 10 80.53061782 3 13 80.53575968 9 16 80.53646211 7 6 80.53840902 10 14 80.54471557 8 17 80.54999575 4 6 80.55595911 3 7 80.57447529 10 9 80.60625049 10 15 80.60979166 5 17 80.62456539 3 14 80.64172712 4 16 80.64731192 9 17 80.64956364 9 7 80.65449645 7 18 80.65677954 8 6 80.67699682 6 18 80.68791074 8 18 80.6903935 10 16 80.69479229 2 10 80.71819529 11 12 80.72092412 5 5 80.72263064 10 8 80.72384377 2 9 80.72785878 6 5 80.72835281 11 13 80.73101795 11 11 80.73797627 3 6 80.74528991 2 11 80.74589905 11 14 80.76518663 3 15 80.77080883 9 18 80.78010952 2 8 80.78083121 11 10 80.78602348 5 18 80.79406215 10 17 80.7982011 4 5 80.80420918 2 12 80.80618377 4 17 80.80798418 7 5 80.80949714 11 15 80.82098863 7 19 80.82389497 8 19 80.84753586 6 19 80.86490623 11 9 80.86987017 9 6 80.8718589 2 7 80.88442106 10 7 80.89072398 2 13 80.89521572 11 16 80.89649164 10 18 80.91883783 3 16 80.92107847 9 19 80.92719625 8 5 80.95566253 5 19 80.98083557 3 5 80.98592089 4 18 80.98699683 11 17 80.99017626 11 8 80.99547858 12 12 80.99802945 12 13 80.99930907 7 20 81.00726683 2 14 81.00993578 8 20 81.02074604 12 11 81.02367561 12 14 81.02443845 2 6 81.04748512 10 19 81.05579806 6 20 81.05833284 5 4 81.05998882 12 15 81.07097145 6 4 81.07317018 12 10 81.08010165 9 20 81.09014789 3 17 81.0910182 11 18 81.10085972 10 6 81.11576742 4 4 81.13409702 12 16 81.13697138 2 15 81.14791069 9 5 81.15806896 7 4 81.16175408 11 7 81.1701797 12 9 81.17211715 1 10 81.17605136 1 9 81.17757827 4 19 81.18343803 5 20 81.1842012 7 21 81.20640475 10 20 81.20840576 8 21 81.20953636 1 11 81.21202798 12 17 81.22091487 1 8 81.22255063 11 19 81.22763573 6 21 81.26769665 9 21 81.26847854 3 18 81.27944177 2 5 81.28050685 1 12 81.28072123 13 13 81.30268414 12 8 81.30568956 2 16 81.30721197 3 4 81.3083352 13 12 81.31018062 8 4 81.3153305 1 7 81.31827681 13 14 81.31880395 12 18 81.32161559 13 11 81.34437508 13 15 81.35608836 11 20 81.36982706 10 21 81.37617582 1 13 81.37829637 4 20 81.39661938 11 6 81.40285458 5 21 81.40366087 13 10 81.40912741 10 5 81.40947838 13 16 81.41259539 8 22 81.41357844 7 22 81.4209766 12 19 81.43816426 9 22 81.46186268 1 6 81.4736132 3 19 81.48543368 2 17 81.48631904 13 17 81.48679665 12 7 81.48815515 5 3 81.49176291 6 22 81.49266094 1 14 81.50169277 13 9 81.50925303 6 3 81.51224971 9 4 81.52510996 11 21 81.52694827 4 3 81.55854957 10 22 81.55878449 12 20 81.56988133 13 18 81.57750121 2 4 81.59545191 7 3 81.60811467 4 21 81.62603781 8 23 81.63267956 14 13 81.63823112 5 22 81.63887255 14 14 81.64538713 1 15 81.64847515 13 8 81.65072527 7 23 81.65078469 14 12 81.65444996 9 23 81.67011159 14 15 81.67345987 13 19 81.68379561 2 18 81.68404223 14 11 81.69713185 11 22 81.69867627 1 5 81.69904256 11 5 81.70401222 3 20 81.70830097 12 21 81.71627982 14 16 81.72050108 3 3 81.72545794 12 6 81.72840023 6 23 81.73302229 10 23 81.75604604 0 9 81.75869108 0 10 81.76525109 8 3 81.76893901 14 10 81.77014323 10 4 81.78384446 14 17 81.78497631 0 8 81.79570591 13 20 81.80499675 0 11 81.8094434 1 16 81.81671246 13 7 81.84088626 14 18 81.86568883 8 24 81.86676378 4 22 81.87134534 12 22 81.87703601 14 9 81.87830608 0 7 81.88360422 11 23 81.88482711 0 12 81.88648009 5 23 81.88962634 9 24 81.89315468 7 24 81.89574683 2 19 81.8994618 13 21 81.94061479 3 21 81.94753511 14 19 81.96171984 10 24 81.96789416 9 3 81.98592406 6 24 81.9886914 0 13 81.99252496 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 (edited) I wasn't happy with the "straight up, diagonal across, straight down" approach, it seemed too obvious. So I 'flattened' the room in the attached diagram which now makes it obvious that a different route is shorter. Edited January 23, 2009 by solarfish Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted January 23, 2009 Report Share Posted January 23, 2009 [spoiler=Wow, your drawing is better then mine. ] Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 (edited) [spoiler=Wow, your drawing is better then mine. ] Use a tool that can do scale drawings and you don't even have to do the maths Edited January 23, 2009 by solarfish Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 Since the question is "walk", you can subtract 8ft for the spider walking the wall. Being a spider, he could spin a web and lower himself from the ceiling. That makes the answer (to part 1) ~76ft Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 23, 2009 Author Report Share Posted January 23, 2009 I wasn't happy with the "straight up, diagonal across, straight down" approach, it seemed too obvious. So I 'flattened' the room in the attached diagram which now makes it obvious that a different route is shorter. You and the good Professor both avoided the 3 4 5 trap that leads to 80 feet. Good job both. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 (edited) Since the question is "walk", you can subtract 8ft for the spider walking the wall. Being a spider, he could spin a web and lower himself from the ceiling. That makes the answer (to part 1) ~76ft If you were going to allow that then the spider would walk diagonally up the first wall, then diagonally across the ceiling to the corner and then drop down. Which would be 73.75 feet approx. Edited January 23, 2009 by solarfish Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 23, 2009 Report Share Posted January 23, 2009 If you were going to allow that then the spider would walk diagonally up the first wall, then diagonally across the ceiling to the corner and then drop down. Which would be 73.75 feet approx. Joke's on both of you. He's a spider, he doesn't walk, he crawls. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
There's a spider lurking on the floor in the corner of a room.
A fly comes to rest on the diagonally opposite corner of the floor and falls asleep.
The spider sets out for the fly; but for his own safety, he does not walk on the floor.
If the room is 40' x 56' with an 8' ceiling, how far must the spider walk for his lunch?
What if the floor is only 4' x 6'?
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