The variation I’m more familiar with (found in Zork, Adventure, a few of the Scott Adams games, etc, but also Anchorhead and various modern games too) is there’s a particular barrier that you can’t bring anything past, and you need one or more specific inventory objects on the other side. The Scott Adams system even had a special opcode for “stop the player if they’re carrying anything” for these puzzles!
The most ancient and venerable version is that you need a way to get your light source through to see what’s on the other side, but it can be used for other purposes as well; in Savoir-Faire it’s used to keep the endgame fast-paced by removing most of your inventory (you can’t carry anything into the endgame region but can wear things) and thus cutting down on all the combinatorial options. You know you only have these three objects to solve the puzzle with, so what do you do with them?
This is one of my favorite puzzle setups, and I’ve used it pretty much everywhere I can; Enigma of the Old Manor House has the classic “get your light source through an inventory-restricting barrier” version, Scroll Thief has a library security scanner that won’t let you carry books through without checking them out first, and Death on the Stormrider has a room that allows carried things but not pushed things (and you need to push a large object to the other side of the map to use it as a step).