My first thought is maybe you should try out some other games.
Hey! That's my Fish! is a popular game for all ages, simple enough for young'uns yet it has some real depth to it.
Ok, that said, here's a kernel of an idea...
Suppose you each have half the mystery, and you're not allowed to just tell the other person. Somehow, you need to give each other clues. If you're less interested in it being a strategic 'game' and just want something for you and your daughter to do together, maybe a 'guess who' style thing where whenever you enter a new room you can ask the other player 'Was it Ms. Scarlet?' 'Was the weapon made of metal?' etc.
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