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Five Cards Trick

July 29th, 2009, 4 Comments

While the magician was sitting in a separate room, his assistance asked an audience to pick 5 cards arbitrarily from a deck of 52 cards. The audience giave the cards back to the assistant who glance the cards quickly. The cards were . He asked the volunteer to keep the and a showed to everybody [...]

Functional Equation

June 27th, 2009, No Comments

Find the functions that satisfy for all where . Solution The above equation can be rewritten as . Interchange between and we have . It follows that ,  hence . Since the left hand only depends on and the right hand only depends on , then the two must be a constant, say . So [...]

Minimizing The Greatest Relative Error

June 27th, 2009, No Comments

Suppose we have a measurement . We don’t know the exact value of . What we know is the bounds of ; . Suppose we approximate with , then the maximum of the relative error is given by We are interested in finding the value of that minimize the maximum relative error. In other word [...]

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