<pre>
Let n be a positive integer.  Define the function f from Z^n to Z by
f(x) = x''1+2x''2+3x''3+...+nx''n.  For x in Z^n, say y is a neighbor of x
if y and x differ by one in exactly one coordinate.  Let S(x) be the
set consisting of x and its 2n neighbors.  It is easy to check that
the values of f(y) for y in S(x) are congruent to 0,1,2,...,2n+1 (mod
2n+1) in some order.  Using this, it is easy to check that every y in
Z^n is a neighbor of one and only one x in Z^n such that f(x) is
congruent to 0 (mod 2n+1).  So Z^n can be tiled by clusters of the
form S(x), where f(x) is congruent to 0 mod 2n+1.
</pre>
