I have dreamed up some ideas for a card game, with one (fairly big) problem. (Actually, I'm sure there are more problems, but I'd have to get over this one to playtest it!).
In order to work you would have to randomly assign matching pairs of cards (or it would work equally well with tiles) to people at the start. Its important that no-one knows what each other has.
e.g.
Player 1 gets both red queens
Player 2 gets both black kings etc.
You cant just shuffle and deal the deck or people wont get matching pairs.
You could deal out one of the pair and get everyone to secretly take a card that matches it, but people who selected their cards later would know which cards were missing, and could be able to work out what others had.
You could pair up the cards and place them face down on the table then randomly assign them, but the person who sorted them might remember where they put them and know who had which cards.
Any ideas?