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Chess Algebraic Notation, Combinations, Openings, Mate in One Puzzles

So with 32 pieces and 64 squares, how many different combinations of games can be played on a chess board?


Magic of Nines with Digital Roots

Remember, that the digital root of a number is the number obtained by adding all the digits, then adding the digits of that sum, and then continuing until a single-digit number is reached. Zero can never be a digital root only 1,2,3,4,5,6,7,8 and 9.


Fractals from Triangles, Quadrilaterals, Inscribed Circles, and Squares

Fractals are self-similar objects. What does self-similarity mean? If you look carefully at a fern leaf, you will notice that every little leaf - part of the bigger one - has the same shape as the whole fern leaf. You can say that the fern leaf is self-similar.

Pascal's Prime Number Multiple Fractals: 2 (and odds),3,5,7,11,13,17

My favorite discovery in Pascal’s are the fractals first found by Sierpinski in 1915 (almost 300 years after Pascal); it is referred to as Sierpinski’s Triangle and is created by coloring in the even numbers (numbers that end in 0,2,4,6,8). It is also quite beautiful to color in the odd numbers (numbers that end in 1,3,5,7,9); you will get a negative image of Sierpinski’s Triangle.