  The puzzle method was introduced by Choi and Park as an effective method for
finding non-singular characteristic maps over wedged simplicial complexes
$K(J)$ obtained from a given simplicial complex $K$. We study further the mod 2
case of the puzzle method. We firstly describe it completely in terms of linear
algebraic language which allows us to develop a constructive puzzle algorithm.
We also analyze our algorithm and compare its performances with other known
algorithms including the Garrison and Scott algorithm.
