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Big Numbers

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Using the standard arithmetic operations (addition, subtraction, multiplication, division and exponentiation), what is the largest number you can make using three copies of the digit “9”? While this would be a pretty large number, with a little cleverness you can do far better. This session explores VERY large numbers!

Catalan Numbers

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Suppose you have n pairs of parentheses and you would like to form valid groupings of them, how many groupings are there for each value of n? How many “mountain ranges” can you form with n upstrokes and n downstrokes that all stay above the original line? What about counting...

Coloring

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Consider a 9 × 9 chessboard, and you wish to cover as much of it as possible using figures shaped like the one to the right, where each of the four squares is the same size as the squares on a chessboard. The pieces can be rotated or flipped over....