We present two new results on Wythoffâ€™s Grundy function G. The first one is a proof that for every integer g 0, the g-values of G are within a bounded distance to their corresponding 0-values. Sinceâ€¦ (More)

A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles.â€¦ (More)

We prove that the smallest covering code of length 8 and covering radius 2 has exactly 12 words. The proof is based on partial classi cation of even weight codewords, followed by a search for smallâ€¦ (More)

A sequence of binary words of length n is called a cube dominating path, if the Hamming distance between two consecutive words is always one, and every binary word of length n is within Hammingâ€¦ (More)