  The authors present formulas for the previous player's winning positions of
two variants of restricted Nim.
  In both of these two games, there is one pile of stones, and in the first
variant, we investigate the case that in k-th turn, you can remove f(k) stones
at most, where f is a function whose values are natural numbers. In the second
variant, there are two kinds of stones. The Type 1 group consists of stones
with the weight of one, and the Type 2 group consists of stones with the weight
of two. When the total weight of stones is a, you can remove stones whose total
weight is equal to or less than half of a.
