Impossible Dove Tail Blocks

The mysterious, impossible dove tail blocks come apart easily

     This is a little curiosity piece i planed to build for christmas presents.   I was going to put a pin through the top center of the blocks and all the way through to the other side.  This pin would be removable.  The curious thing about this block is it is actually two blocks, dove tailed together.  The other side of the assembly looks identical to this one.  But what makes it mysterious is the fact that they can be taken apart quite easily, despite the "locked in" appearance of opposing dove tails.  The blocks were assembled AFTER cutting both dove tails.  How did i do it is the big question here?

(rendered models)