17.4 Northcott’s variation of Nim 511
17.4 Northcott’s variation of Nim ...........
Two players alternately move their counters on one of the rows, the only
restriction being not moving onto or beyond the opponent’s counter. The
one who cannot move loses.
This is equivalent to nim if one considers a number of piles of coun-
ters corresponding to the number of spaces between the counters on the
rows. (If a player tries to increase the number of spaces, the other player
can force the same distance by pursueing the same number of spaces).
Therefore the player who can balance the nim sum equation has a win-
ning strategy.
For example, in the above arrangement, the numbers of spaces have
nim sum
3 2 4 2 2=5.
It can be made 0 by moving 3 spaces in row 3.