Code Correction

a puzzle game based on parity and hamming codes. each puzzle is randomly generated. first a binary code is generated. then a binary key is created based on the original binary code. finally a single digit within the original binary code is inverted. using the key you must find the binary digit that was inverted. modes 2x2 = 2^(2*2)*2*2 = 64 possible combinations 4x4 = 2^(4*4)*4*4 = 1,048,576 possible combinations 8x8 = 2^(8*8)*8*8 = over 1,180,000,000,000,000,000,000 possible combinations 16x16 = 2^(16*16)*16*16 = a very large number. 32x32 = 2^(32*32)*32*32 = more puzzles than any human can solve in a lifetime.