3. On the blackboard, it is written
$$
1!\times 2!\times \cdots \times 2011!\times 2012!\text {. }
$$

If one of the factorials is erased so that the remaining product equals the square of some positive integer, then the erased term is . $\qquad$
3. 1006 !.

Notice that the given product equals
$$
\begin{array}{l}
1^{2012} \times 2^{2011} \times \cdots \times 2011^{2} \times 2012^{1} \\
=\left(1^{1006} \times 2^{1005} \times 3^{1005} \times \cdots \times 2010^{1} \times \\
2011^{1}\right)^{2} \times 2^{1000} \times 1006!
\end{array}
$$