You have a block of wood 1 by 2 by 7 units. One of the 2 by 7 faces has 2 nails inserted, the heads and part of the shaft of each nail protruding. If the coordinates of the corners of this face are: (0,0), (0,2), (7,2), and (7,0), then the nails are located at (1,1) and (6,1).

Assume the coefficient of friction between string and wood is zero, and that the diameter of the nails is negligible.

(1) The ends of a non-elastic string of length 13 units are attached, one end to each of the 2 nails. The string is taut. How is this possible?

(2) What about a second piece of taut string, approximately 8.544 units long, also with ends attached to the 2 nails?

(3) What about a third piece of string approximately 22.0880 units long?

Part (1):  With the nails 5 units apart and a 13 unit string; a 5/12/13 triangle comes to mind.

Connect the first string, route it around the block twice, via the 1 and 2 unit sides. Connect the string to the second nail  This gives (1 + 2 + 1 + 2) x 2 = 12 units of distance in traveling around the block. Total distance is:

5^2 + 12^2 = 13^2

Now for the others . . .

Posted by Leming on 2005-08-08 15:28:59