Exam: Sherman Exam
Are you a first year student? Do you like Math? Do you like a challenge?
The come and participate in the Sherman Prize Exam! The Sherman Prize Exam consists of challenging, but not impossible, math problems. All you'll need is the desire to have fun with math puzzlers, and a pencil. contact Professor Christopher Rasmussen (firstname.lastname@example.org) if you have any questions. If you can't make the time, we can work something out.
To give you an idea of what this exam will be like, here are two sample problems suitable for the Sherman prize exam:
Define a neighbor of a square S on a standard 8x8 chessboard to be any square that shares an edge with S. In each square of the chessboard, a number is placed. Suppose that, for every square S, the number placed in S is equal to the average of the numbers placed in the neighbors of S. Prove that all of the numbers placed on the chessboard are equal.
A quadrilateral Q is inscribed in a rectangle R so that each side of R contains exactly one vertex of Q. Show that the length of the perimeter of Q is at least twice that of the diagonal of R.
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- Exley Science Center Tower ESC 109
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