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1   Water and Wine

• Water and Wine

2   The Chessboard Problem

• The Chessboard Problem

3   Knight's Tour

• Knight's Tour (8x8)
• Knight's Tour (8x8) - Closed Path

4   Can an Irrational Number to an Irrational Power be Rational?

• Irrational Number to an Irrational Power

5   What is John's Favorite Number?

• What is John's Favorite Number?

6   Stairway to Heaven

7   Pennies from Heaven

• Pennies from Heaven

8   The Simplest Irrational Number and a Challenge

9   Sum of Polynomial Coefficients

• Sum of Polynomial Coefficients
• Summation Formulas with Binomial Coefficients
  • The Sum k (n choose k)
  • The Sum k^2 (n choose k)
  • The Sum 1/(k+1) (n choose k)

10   Matrix Power Challenge

• Raise a 3x3 Matrix to the Power of 2017