Problem of the day 1 oct 2011

In 3-dimensional space, there are 3 rays leaving point . Any pair of 2 rays make a 60 degree angle with each other in their respective planes. Points , , and  are situated on the rays (one per ray) such that , , and  are all integers, and . if  and  is odd, then determine the value of  if .






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Problem Of The Week 10

Find the length of the shortest path from (0,0) to (12,16) in the x-y plane which does not go inside the curve x^2-12x+y^2-16y+75=0