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Here is a piece of plywood in the shape of an isosceles triangle. The side lengths are 1, 1, sqrt(2) units. Quick and dirty representation: A | \ | \ | \ | \ B--------------C The angle at B is a right angle. We'd like to cut this into two pieces of equal area. There are many ways to do this with a single cut. Which cut has the shortest distance?

In a game of "simplified football," a team can score 3 points for a field goal and 7 points for a touchdown. Notice a team can score 7 but not 8 points. What is the largest score a team cannot have?

These problems use Knuth's up-arrow notation (http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation), with ^ being the up-arrow. 1. Find the smallest value for n, such that 1000^^n > 12^^(n+1). 2. We define the sequence g, by assigning g(1) = 3^^^^3, and g(n+1) = 3^^^...^3, where the number of up-arrows is g(n). A famously large number is Graham's number = g(64). Which is larger, Graham's number or 2^^^...^2, where the number of up-arrows is Graham's number?

If P(x) and Q(x) have 'reversed' coefficients, for example: P(x) = x5+3x4+9x3+11x2+6x+2 Q(x) = 2x5+6x4+11x3+9x2+3x+1 What can you say about the roots of P(x) and Q(x)?

what dus the poor man have,the rich man need,and the dead do