ABSTRACT
Turnips have a richer theory, but it is a great pity that the full theory is only needed by people wealthy enough to play with a very large number of coins. In a move of Grunt game one must turn over four symmetrically arranged coins of which the first must be the leftmost coin of the game and the last must be turned from heads to tails. In the two-dimensional games the corresponding requirement is that the most “south-easterly” coin which is turned must go from heads to tails. Since the nim-values for Motley are exactly the powers of 2, and each nim-value for Streaking is the mex of all numbers that are sums of earlier nim-values from the same row or earlier nim-values from the same column. For convenience, and to avoid cruelty to turtles, the reader may play these games with coins.
