Recent content by Canada_Whiz

Aruna is (respectfully) wrong. The real minimum occurs when x=7.5, which gives y=12.99 This can be found legitimately (as opposed to aruna's hand-wavy argument) using similar triangles.

So for AP Bio, my teacher is assigning extra credit if we can find an article or journal entry that suggest the current status of the cell- the Fluid Mosaic model- might be changed to form a more accurate description. He said that they are suggesting it should be more mosaic and less fluid...

Seeing as the test day for the 2011 Pascal Contest was yesterday, let's discuss! My answers: B>E>C>B>A A>B>D>E>C E>D>A>C>A D>A>C>E>D D>C>B>A>C Now I was not sure about problems 20,24, and 25 If anyone remembers the wording of the problems, can you please post them? In fact, can anyone...

Thanks guys! But can anyone provide a rigorous proof? For example, hgfall, you proved that i can always guess the number in 1007 moves, but you haven't proved that is the ABSOLUTE MINIMUM number of moves for which I am guaranteed to guess the number. So a rigorous proof would be appreciated =)

Fun Game Theory, Guessing a Number With a "Twist" You and I are playing a game. I begin by picking an integer from 1 to 2011 (inclusive). On each turn you try to guess my number. I then tells you whether your guess is too high, too low, or correct. If your guess is not correct, I add or...

There are 10 paths for n=4. I have found the answer, and to quench your curiosity, here it is :) http://www.artofproblemsolving.com/Forum/viewtopic.php?f=41&t=382116

Suppose an ant is on a vertex of a cube. On one of the three vertices neighboring the ant, there is a black hole. On each move, the ant travels to one of it's neighboring vertices, being careful not to pass through the black hole. The ant makes N moves in total. How many different paths lead the...

To prove the circles formed by ABC and ABD are the same, we just need to prove that <ACB+<ADB=180. Can anyone tell me how to do that?

Thanks for all the interest in this problem, but does anyone know where to start? Coordinate bashing is WAY too ugly.

Ok i did that and got INCREDIBLY messy coordinates for the intersection points, not to mention I have no idea how to even find the tangent points of the common tangent. There has to be a purely synthetic solution. Thanks :)

You have to prove the radius is the same regardless of how my friend and I draw our circles. So like if we put the circles really close or really far apart, it will be the same radius (given that the circles still intersect at two points)

Geometry Problem Involving Circles and Fixed Radius- Please Help! I have a compass with radius X, and my friend has a compass with radius Y. We both draw a circle with our compasses so that our circles intersect at two points. Call these two points C and D. You draw a common tangent to both...

Trignometry Proof Help! If a,b,c are sides in a triangle such that a<1/2(b+c) show that angle A (the angle opposite to side a) is less than 60 degrees

As you might know, the 2010 Euclid Contest was officially taken yesterday. So let's discuss! I thought it wasnt too bad. #10 was hard though (the triangle one). Here was the question: For each positive integer n, let T(n) be the number of triangles with integer side lengths, positive area...