Thirteen Diamonds

getting home and wondering where I was and why dinner wasn't ready.
    Carol saw my action and said, “You'll be home soon enough. Your theory, apparently, is that the shellfish was added to the casserole during the fire alarm evacuation. You went all the way to San Diego to dig up some dirt on Ellen, but she has an iron-clad alibi. So who does that leave as a suspect—Ida?”
    I didn't dignify her question with an answer.
    Carol looked me straight in the eye and said, “I suspect that you suspect somebody other than the people we've named so far.” The pencil she had been playing with snapped. “Let's investigate this a little further. You took the trouble to find out that Gerald's bequest to Silver Acres was $500,000, not $100,000, as I had said.
    “Then somehow my calendar book disappeared from my purse at Albert's house and then reappeared at my office. This sort of thing doesn't usually happen without some human intervention. And Wesley is suddenly scrutinizing the Silver Acres books, even though he's shown little interest in them during the year-and-a-half he's been president of the residents' association. However, he won't find anything.”
    “What are you driving at?” Joe asked.
    “Lillian thinks that I had something to do with putting the shellfish in the casserole.”
    “But that's not true!” Joe said.
    “Of course not. But you know how these old ladies are when their minds start to go.”
    “We were both in our offices when the alarm went off,” Joe said, looking at Carol. “Somebody turned on the alarm switch by the reception area, but since Ophah was at lunch we don't know who. We were both on the phone and by the time we hung up and came out of our offices the person had disappeared—apparently down the corridor leading to the dining room. Or maybe the alarm switch was faulty.”
    That sounded suspiciously like the gospel according to Carol.
    Joe continued, “The established procedure is for Carol and me to clear everybody out of the building. We started at the reception area and covered the whole building.”
    “Do you each have your own route to clear the building,” I asked, trying to gain some control, “or do you go together?”
    “We go separately,” Joe said before Carol could speak. “It's faster that way.”
    “Was Carol carrying anything when you started out?” I asked.
    “Nothing,” Joe said, positively.
    I hoped that Albert would call and I wanted to waste time, so I said, “Clearing the building reminds me of a problem in topology that goes like this: The city of Bridgeton has a river running through it with two islands in the river. One bridge connects the two islands. Four bridges connect one island with the mainland, two to each side of the river. Two bridges connect the other island to the mainland, one to each side of the river. Starting from wherever you wish, is it possible to cross all seven bridges without crossing any one bridge twice?”
    “That's all very interesting,” Carol said, sarcastically, “but hardly relevant to the current discussion.”
    “Not true,” I said. “The layout of this building is two long corridors, parallel to each other, with three cross corridors connecting them, two at each end and one in the middle. A short corridor runs parallel to the two long ones, from the reception area to the center cross-corridor and the dining room. Sort of like a boxy eight with an extra vertical line. Similar to but not as complicated as the puzzle.
    “Rooms go off from each of the corridors. Your offices are at the two corners of one end of the building, with the reception area in between. If you each started your patrol from the reception area and covered all the corridors, between you, at least one of you had to double back, meaning re-cross a bridge, at some point.
    “You're right,” Joe said. “Carol went up the corridor behind the reception desk to the dining room and then over the center cross corridor to the long corridor. There are a couple of rooms between that corridor and her office.”
    “So she had to backtrack toward her office.”
    “Yes.
    “Where did you go?”
    “I went up the other long corridor all the way to the end and took the last cross corridor over to the recreation room.”
    “Did you beat Carol there?” I asked.
    “Yes. She was still checking the library, which is beside the rec room, when I got there. I started back toward the front and passed her as she came out of the library.”
    “Was she carrying