Making roads

You are an engineer in the middle of a small and beautiful village with mountains looming in the background. They have a mud road and insist on building another thats perfectly perpendicular to the first one. Skanda's house is on the original road and the new road intersects in front of his house. Like all spirited people, they want to test your college education and give you a long rope. How do you find the right angle?

In other words, given a long rope, how can you fold it into a right-angled triangle?

I am tempted to give you a hint but GOD, someone please attempt a solution... :-)

Power balance

A chess board has 64 squares. Pick numbers between 1 and 64 and place these numbers on each of the squares of the chess board such that the value in every square is the average of the values of its neighboring squares.

Prove that the only way to make such an arrangement is when all squares have equal numbers.

(http://www.cisl.columbia.edu/grads/tuku/brainteasers.html)