I had the same problem with the 3'x1' 1000 piece puzzle of the 4 houses and the Hogwarts crest. The box contained 1000 pieces alright but two of them were for the same opening. Trace the open space of the missing piece, cut thin cardboard layers and glue together until the piece has the same thickness as the other pieces minus one layer. The picture of the completed puzzle on the box cover can be photocopied and the needed area enlarged so the colors and pattern fit will be perfect. The trick is sizing and I find librarians are very helpful if your home equipment is not up to the task. Cut out the exact part you need, glue to the cardboard piece you have prepared and apply a very thin coat of clear nail polish if the puzzle has a shiny surface you need to match. Let dry completely before framing. Think of it as getting two activities to enjoy for the price of one. Then invite your friends to try to find the piece you created!
The puzzle was alot smaller than expected especially for the price. It was fun to do and very challenging. At the end, however, there was a piece missing so the puzzle is left incomplete.