Lord Darcy determines where the hidden door is.

Lord Darcy is visiting at Lord Vauxhall's estate. Lord Vauxhall seems to be delayed joining with his guests. A search ensues for Lord Vauxhall. It is noticed that all the lights are on in Lord Vauxhall's summer cottage away from the main mansion. The doors to the cottage are all locked and the windows are all varnished so that no one can enter through the windows. By looking through the windows, Lord Vauxhall can be seen laying on the floor in the room labeled B below.

The locksmith for Lord Vauxhall is summoned and the cottage is entered. Lord Vauxhall is examined. He had died of sudden old age. The only set of keys for the cottage are found with Lord Vauxhall's body and each of the sixteen keys is to a separate door in the cottage. Each key had been used only once that evening and each door was gone through and relocked from the other side.

Here is a schematic of the cottage with the rooms labeled with letters.

What is the letter of the room with the hidden entrance to the cottage used by Lord Vauxhall to enter the cottage that evening?

This problem is based on Randall Garrett's Lord Darcy . The story The Sixteen Keys was first published ion Fantastic in May of 1976