\documentclass[12pt]{article}
\usepackage{amsmath,mathrsfs,bbm}
\usepackage{amssymb}
\textwidth=4.825in
\overfullrule=0pt
\thispagestyle{empty}

\begin{document}
\noindent
%
%
{\bf Urban Larsson}
%
%

\medskip
\noindent
%
%
{\bf Blocking Wythoff Nim}
%
%

\vskip 5mm
\noindent
%
%
%
%
The 2-player impartial game of Wythoff Nim is played on two piles of
tokens. A move consists in removing any number of tokens from
precisely one of the piles or the same number of tokens from both
piles. The winner is the player who removes the last token. We study
this game with a blocking maneuver, that is, for each move, before the
next player moves the previous player may declare at most a
predetermined number, $k - 1 \ge 0$, of the options as forbidden. When
the next player has moved, any blocking maneuver is forgotten and does
not have any further impact on the game. We resolve the winning
strategy of this game for $k = 2$ and $k = 3$ and, supported by
computer simulations, state conjectures of `sets of aggregation
points' for the $P$-positions whenever $4 \le k \le 20$. Certain
comply variations of impartial games are also discussed.



\end{document}

.
