  Here, we present a variant of Nim with two piles. In the first pile, we have
stones with a weight of 1, and in the second pile, we have stones with a weight
of -2. Two Players take turns to take stones from one of the piles, and the
total weight of stones to be removed should be equal to or less than half of
the total weight of the stones in the pile. The player who removed the last
stone or stones is the winner of the game. The authors discovered that when
(n,m) is a previous player's winning position, 2m+1 is the last remaining
number of the Josephus problem, where there are n -numbers, and every second
number is to be removed. There are similar relations between the position of
which the Grundy number is s and the (n-s)-th removed number.
