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Straighten the paper clip and slip it inside the binding of an old copy of Britannica I have. I got it second hand from a public library, so it has quite a few of the old style anti-theft tags hidden throughout; it also contains quite a few paper clips of many colors I once used as bookmarks.
I use the remaining time to clean the house, making sure to go into the bathroom more than once, moving the toilet tank lid and opening and shutting all of the cabinets every time. If I'm very lucky I'll be just shutting the medicine cabinet audibly when the investigators walk in. (For those not familiar, many houses built in the mid 20th century in the US had slots in the back of the medicine cabinet where you were supposed to dispose of used razor blades.)
I think they'd tear the entire house apart trying to find that thing. There's a small chance someone would notice paper clips on the Brittanica and start checking for more. Whether they find it depends on whether they have access to x rays or a metal detector.
I have no doubt that they would, but that's not one of the variables I'm trying to control. As far as I can tell, time and volume are the only two things that I can play with. They have a 30-minute timer, and cannot take the load-bearing walls down. That means there's a volume constraint, no matter how many people they have available they can only fit so many in one space. That limits the amount of time they have to actually search, assuming they empty the dwelling. If they don't empty the dwelling, it sharply limits the number of people they can have searching at any one time. Heavy equipment like an x-ray machine also limits that volume.
With respect to the Britannica, if you're familiar with them you know they are massive and this one just happened to be my primary research source in high school. I cannot understate the number of flags and paper clips simply destroying those bindings right now. If someone does notice it, I'm relying on running out the clock with them checking every one they see first.
They'd have to stay within the home, but they do have 12 hours to check through things. So, they cannot empty the things to the outside, they have to sort through things inside. I guess that eliminates the xray idea.
But a metal detector and 12 hours time would put the odds in their favor.