TimeSpaceLightForce Posted January 26, 2014 Report Share Posted January 26, 2014 An ant at A trails the shortest track from A to B on the sugar cubes structure as shown. Then it went through the shortest tunnel from B to A. How far it travelled to B and back to A? Quote Link to comment Share on other sites More sharing options...
0 Perhaps check it again Posted January 26, 2014 Report Share Posted January 26, 2014 (edited) This problem isn't presented clearly. 1) The shortest track from A to B ON the sugar cubes might entail going through the tunnel and ON the sugar cubes. 2) "Through the shortest tunnel!?" There is only one tunnel. That is, there is only one hole. If you mean going from A to B *without* passing through the hole (and be the shortest route), then you're going to have to state that. And then if you mean the return trip from B to A must pass through the hole (and be the shortest route), then you are going to have to state that as well. An ant at A trails the shortest track from A to B on the sugar cubes structure as shown. Then it went through the shortest tunnel from B to A. How far it travelled to B and back to A? Edited January 26, 2014 by Perhaps check it again Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted January 27, 2014 Author Report Share Posted January 27, 2014 This problem isn't presented clearly. 1) The shortest track from A to B ON the sugar cubes might entail going through the tunnel and ON the sugar cubes. 2) "Through the shortest tunnel!?" There is only one tunnel. That is, there is only one hole. If you mean going from A to B *without* passing through the hole (and be the shortest route), then you're going to have to state that. And then if you mean the return trip from B to A must pass through the hole (and be the shortest route), then you are going to have to state that as well. An ant at A trails the shortest track from A to B on the sugar cubes structure as shown. Then it went through the shortest tunnel from B to A. How far it travelled to B and back to A? there are 2 paths "on" surface and "through" tunnel.. the 2X1X1 hole is NOT the tunnel. Quote Link to comment Share on other sites More sharing options...
0 KMS-Windsor Posted January 28, 2014 Report Share Posted January 28, 2014 Does "tunnel" mean the tiny gap between the cubes? From B, he still need to travel on a surface to get to a gap between 2 cubes. Is that acceptable? Quote Link to comment Share on other sites More sharing options...
0 kukupai Posted January 28, 2014 Report Share Posted January 28, 2014 The shortest way from A to B is a bit more than 5,84 units (red line in the left picture). From B to A the ant travels by the diagonal of an imaginary plane between lines ef and ab (folded a bit at the line cd) - yellow line in the right picture. Should be some 5,49 units or so. Maybe. Sorry for my English. 1 Quote Link to comment Share on other sites More sharing options...
0 plainglazed Posted January 29, 2014 Report Share Posted January 29, 2014 i cant fully visualize this just yet but think the ant can travel ever so slightly shorter than kukupai's answer above (34).5 EDIT: 1 Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted January 29, 2014 Author Report Share Posted January 29, 2014 (edited) Well done kukupai & plainglazed...nice illustration! Edited January 29, 2014 by TimeSpaceLightForce Quote Link to comment Share on other sites More sharing options...
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TimeSpaceLightForce
An ant at A trails the shortest track from A to B
on the sugar cubes structure as shown. Then it
went through the shortest tunnel from B to A.
How far it travelled to B and back to A?
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