The timing of the theft and the restrictions on entry to the house limit the suspects to the three who left the parlor. Santa had no time alone with the sack in the library, where the thief discarded the box and the wrapping.
Since the necklace was one of the last gifts to be put in the safe, it was one of the first to be put in the sack, at the bottom. The thief therefore had to spend at least a few minutes looking through over twenty presents for it. This rules out Sara, who was out of the parlor very briefly.
The thief clearly looked for the gift to Susan. Even someone who had not attended a Stone party before could have surmised that Richard’s gift to his wife would be the most expensive one. A newly arrived interviewee, however, would not know Susan’s nickname, which was used on the wrapping. An old friend would.
Only Jack Chessler had both the knowledge of the nickname and the time to search for the sack. He was therefore the thief. A book dealer, he had entered the library to see Richard’s newly acquired Poe volume and there had noticed the sack behind the sofa.
Where did he hide the necklace? He could not have taken it outside because of locks and alarms, and the house and the guests’ clothing had been searched. Chessler wore a toupee, however, as Richard had kiddingly noted when greeting him, and it was under the toupee that the small necklace had been hidden. Santa used a little logic and observation, and unmasked the Grinch.