Tuesday, July 15, 2008

54. A simpler web.


Problem 53. is tough. You might be able to wrap you head around this one, then, once you see the principle, give 53. another try. A spider and a fly are on two corners of a triangular web. The spider moves to an adjacent corner randomly once a second. The fly stays put. On average how many seconds does it take for the spider to reach the fly? (2 Points)

Saturday, July 12, 2008

53. The Bucky Spider


An fly and a blind spider are on opposite corners of a buckyball (Carbon 60, a soccer ball shape). The fly is stationary and the spider moves at random from one corner to another along the edges only, once a second. On average, how many seconds does it take the spider to reach the fly? (5 Points)

Replace "buckyball" with "cube" and the problem is worth (3 points) .

Replace "cube" with "dodecahedra" and the problem is worth (4 points).

Saturday, July 5, 2008

Problem 52. Golden Pentagon


52. A regular pentagon is circumscribed by a circle of diameter length 1, see diagram.
  • What is the length of line segment AC? (2 points + 1 point bonus without any trig function)
  • What is the area of the pentagon? (2 points)