Consider an L-shaped ditch with straight sides and both legs of the same uniform width.
Part 1: How wide a ditch can be bridged with two 10 foot planks?
Part 2: How wide a ditch can be bridged with three 10 foot planks?
Note: consider the planks to be rigid line segments - very thin yet strong.
By the definition given, the planks still need to be suppoted in two places each or they will "fall" into the ditch. In addition, I am assuming that "bridging" means that the planks form a connected path of some sort accross the ditch - gravity doesn't count, and one does not have to prove you can walk accross the "bridge".
Part 1: use one plank to create a 45/45/90 isosolese triangle with the outer side of the ditch accross the outer corner of the "L". Then use the second plank to connect from the midpoint of the first to the inner corner of the "L" You have spanned a length of 15 ft accross the corners of the "L", therfore the width of the ditch is 15/sqrt(2) or about 10.61 ft. You could walk on this bridge if the planks are strong enough.
Part 2 - first plank as in part 1. Second plank from the outer corner of the "L" through and beyond the midpoint of the first plank. Third plank just reaches the free end of the second plank and coninues to the inner corner of the "L". Diagnol distance accross the corners of the "L" is 20 ft, width of ditch is 20/sqrt(2) or about 14.1 ft. You could not walk across this bridge regardless of the strength or stifness of the planks.
If walking across is required, I am not sure but I think the third plank doesn't help unless you can actaully fasten it rigidly to another plank, which is not allowed by the problem? Or is there a better solution?
Posted by Kenny M
on 2017-08-17 19:55:11