Monthly Archives: January 2020

MATHCOUNTS Exercises – 11

Posted on January 11, 2020 by kevin

As shown in the following figure, a quarter circle is drawn in a unit square, and 3 smaller squares are inscribed inside the quarter circle. Find the total area of the 3 smaller squares. Click here for the hint. Hint … Continue reading →

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MATHCOUNTS Exercises – 10

Posted on January 8, 2020 by kevin

Joseph, Pedro, Samuel and David leave their backpacks by the classroom door. When the alarm rings they rush to leave, each randomly grabbing a backpack on the way out. What is the probability that each boy takes a backpack that … Continue reading →

Posted in Combinatorics, MATHCOUNTS, Probability | Comments Off on MATHCOUNTS Exercises – 10

MATHCOUNTS Exercises – 9

Posted on January 5, 2020 by kevin

A unit cube is painted with 1 face in red, 1 face in green, 1 face in yellow, and 3 faces in blue color. How many unique ways to paint the cube? Click here for the solution. Solution There are … Continue reading →

Posted in Combinatorics, Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 9