TimeSpaceLightForce Posted September 6, 2016 Share Posted September 6, 2016 (edited) What is the least total length of the track that can be traversed by the mouse to go from hole to hole?The pool table is 2 x 1 meter. Edited September 6, 2016 by TimeSpaceLightForce Link to comment Share on other sites More sharing options...
Mordred Posted September 6, 2016 Share Posted September 6, 2016 (edited) 6 metres 5 metres if the mouse doesnt need to return to original hole Edited September 6, 2016 by Mordred Link to comment Share on other sites More sharing options...
TimeSpaceLightForce Posted September 6, 2016 Author Share Posted September 6, 2016 1 2 3 4 5 6 connecting 1-6,3-4,2-5is just 1+2*sqt(5)=5.472 but not short enough.. Link to comment Share on other sites More sharing options...
swansont Posted September 6, 2016 Share Posted September 6, 2016 1 2 3 4 5 6 connecting 1-6,3-4,2-5 is just 1+2*sqt(5)=5.472 but not short enough.. But you haven't connected 6 to anything else. After you go 1-6, how do you get to 3? Chief O'Brien or Scotty using the transporter? 1 Link to comment Share on other sites More sharing options...
TimeSpaceLightForce Posted September 6, 2016 Author Share Posted September 6, 2016 via crossroad.. Link to comment Share on other sites More sharing options...
kisai Posted September 6, 2016 Share Posted September 6, 2016 5 meters going round. Link to comment Share on other sites More sharing options...
swansont Posted September 6, 2016 Share Posted September 6, 2016 via crossroad.. I don't understand what you mean by that. Link to comment Share on other sites More sharing options...
Sensei Posted September 7, 2016 Share Posted September 7, 2016 (edited) 1 2 3 4 5 6 connecting 1-6,3-4,2-5 is just 1+2*sqt(5)=5.472 but not short enough.. Nonsense. You forgot to mention the one important rule in your game.. The way you described above, one could join 1-4,2-5,3-6 (or 1-4,5-2,3-6). And have 3 total length. But there are missing 4-5 and 2-3! Therefor the way you explained game in #1 post, the correct answer is 5. Edited September 7, 2016 by Sensei Link to comment Share on other sites More sharing options...
TimeSpaceLightForce Posted September 7, 2016 Author Share Posted September 7, 2016 @senseiThe mouse makes the tracks or pathway that is as short (total length) as possible to access all 6 holes.It can go to any hole from any hole not necessarily directly or from any hole to the next adjacent hole.It can go back its track not necessarily increasing the length of track. Dont mind the distance it travels. Your proposition will be 5 meters too.. because 1-4-1-2-5-2-3-6 is the "E" route to access all pocket holes.5 meters is wrong because it is not short enough. @ swansontThe mouse can do the 1-6-middle-3-4-middle-2-5.. eventually making the crossroad where it can go back toto access the 6 holes. @ kisai5 meters is wrong because it is not short enough. @ Mordred5 meters is wrong because it is not short enough. Link to comment Share on other sites More sharing options...
Mordred Posted September 7, 2016 Share Posted September 7, 2016 (edited) I don't see any solution shorter than 5. @sensei The mouse makes the tracks or pathway that is as short (total length) as possible to access all 6 holes. It can go to any hole from any hole not necessarily directly .... It can go back its track not necessarily increasing the length of track. Dont mind the distance it travels. . Clarify this with Total length travelled in particular it can go back on its track without adding to total length travelled... 😱 Edited September 7, 2016 by Mordred Link to comment Share on other sites More sharing options...
TimeSpaceLightForce Posted September 8, 2016 Author Share Posted September 8, 2016 @mordred-its ok.. -tracks means path,route,course or trail and has length .. not to be mistaken as accumulated length of foot steps. -no, going back along track will add to total length of travel..not to the track length. HINT : Imagine the pockets are towns.. what is the shortest road system to access all the towns? Link to comment Share on other sites More sharing options...
Mullimanz Posted September 8, 2016 Share Posted September 8, 2016 What about a path from 1-6, with the other 4 town being reached paths branching and perpendicular to the first path? What about a path from 1-6, with the other 4 town being reached paths branching and perpendicular to the first path? No that doesn't work my bad 1 Link to comment Share on other sites More sharing options...
Sriman Dutta Posted September 8, 2016 Share Posted September 8, 2016 Least distance is the perimeter of the whole figure. Link to comment Share on other sites More sharing options...
John Cuthber Posted September 8, 2016 Share Posted September 8, 2016 (edited) Least distance is the perimeter of the whole figure. No it isn't. You can obviously miss out any one link between two holes and still have all of them connected. I'm fairly sure I can do it with 4.828 units Edited September 8, 2016 by John Cuthber 1 Link to comment Share on other sites More sharing options...
TimeSpaceLightForce Posted September 9, 2016 Author Share Posted September 9, 2016 (edited) @mullimanz That is 4.91m..not bad. @John Cuthber Good sample! But not short enough. Edited September 9, 2016 by TimeSpaceLightForce Link to comment Share on other sites More sharing options...
Sensei Posted September 10, 2016 Share Posted September 10, 2016 Angle 120 degrees. Total length approximately 4.73. Link to comment Share on other sites More sharing options...
imatfaal Posted September 10, 2016 Share Posted September 10, 2016 I can do it in 4.76 units Nah - I can do it in 4.66 units. Will post diagram when at full pc Link to comment Share on other sites More sharing options...
Sensei Posted September 10, 2016 Share Posted September 10, 2016 I made SpreadSheet how results changes with various length line from center of table to "middle" of left/right side (A). Here is zoomed in range where it's starting growing: (25 row is the smallest) A is auto-incremented. 1-A is rest. B=SQRT((1-A)^2+0.5^2) Total length 4*B+2*A+1 1 Link to comment Share on other sites More sharing options...
imatfaal Posted September 10, 2016 Share Posted September 10, 2016 a = sqrt (.211^2+.789^2) = .8167 b = sqrt (.211^2+.211^2) = .2984 c = 1/[sqrt(3)] =.57753 d = 1 - 2*(1/[2*sqrt(3)] = 1 - 1/sqrt3 = .4226 2*a+b+4*c+d = 4.664 2 Link to comment Share on other sites More sharing options...
John Cuthber Posted September 10, 2016 Share Posted September 10, 2016 I'm a little surprised that the solution (assuming that's an optimum) isn't symmetrical. Link to comment Share on other sites More sharing options...
TimeSpaceLightForce Posted September 10, 2016 Author Share Posted September 10, 2016 @imatfaal Solved..the 120 degrees network connects n points in space with shortest line segments. Link to comment Share on other sites More sharing options...
imatfaal Posted September 10, 2016 Share Posted September 10, 2016 I'm a little surprised that the solution (assuming that's an optimum) isn't symmetrical. To be honest so am I - decided to check non-symmetrical when I split the puzzle into two to simplify. The LHS connects 3 holes the RHS connects 4 holes - one of both in common; rather than each side connecting 4 with two of each in common And can anyone tell me a nice online app / freeware that would allow me to draw that accurately and easily? Link to comment Share on other sites More sharing options...
Sensei Posted September 10, 2016 Share Posted September 10, 2016 (edited) And can anyone tell me a nice online app / freeware that would allow me to draw that accurately and easily? I was using LightWave 3D. Not free for ordinary user. Although I received it for free. If we select two points and use Detail > Measure > Measure Points, it's calculating length of line, x,y,z abs delta between points. Edited September 10, 2016 by Sensei Link to comment Share on other sites More sharing options...
John Cuthber Posted September 10, 2016 Share Posted September 10, 2016 @imatfaal Solved..the 120 degrees network connects n points in space with shortest line segments. Proof? And can anyone tell me a nice online app / freeware that would allow me to draw that accurately and easily? No, but I used paint which is free and lets you do it really badly. Link to comment Share on other sites More sharing options...
TimeSpaceLightForce Posted September 11, 2016 Author Share Posted September 11, 2016 @John CuthberSorry no proof..and it can not work if there's no need.If we intersect each 3 points with 3 lines forming "Y" @ 120 deg w/ each other,that will be the minimum connecting length. Unless the 3 points are making > 120 anglebecause the lines connecting them is already the minimum. I tried this with the cubic room where a spider web connects the 8 corners .It worksWith 13 segments network.All angles of the adjacent web segment are 120 degrees.e.i. for the minimum length. AutoCAD is the best for this. No math needed. Just click lines to read measurements. 1 Link to comment Share on other sites More sharing options...
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