Consider all binary sequences (sequences consisting of 0’s and 1’s). In such a sequence the following four types of operation are allowed: (a) $010 \rightarrow 1$, (b) $1 \rightarrow 010$, (c) $110 \rightarrow 0$, and (d) $0 \rightarrow 110$. Determine if it is possible to obtain the sequence $100...0$ (with $2003$ zeroes) from the sequence $0...01$ (with $2003$ zeroes).
Problem
Source: MOP 2005 Homework - Blue Group #8
Tags: invariant, combinatorics unsolved, combinatorics