There's a game this made me think of, which I now cannot remember or work out the name of. You had a collection of objects (think coloured plastic triangles, cubes etc.) and one player arranges a few of them into groups, which should all match a secret rule that they have come up with ("more red than blue objects" or "all triangles are stacked on top of cubes"). The other players then have to try and work out the rule, but the rule setter only communicates by giving counter examples if they haven't got the rule right. It was something like that anyway, can anyone remember the name?

The original edition was kind of cheap and plastic feeling, but it's the sort of thing that could be done nowadays with really high quality components.