Sleuth
In Sleuth; a classic deduction game from master designer Sid Sackson originally released as part of the 3M Gamette Series; players are searching for a hidden gem; one of 36 gem cards hidden before the start of the game. The remainder of this gem deck – with each card showing 1-3 diamonds; pearls or opals in one of four colors – is distributed evenly among the players; with any remaining cards laid face up. Thus; you and everyone else starts with some information about what's not missing.
A second deck contains 54 search cards; each showing one or two elements; such as diamonds; pairs; blue opals; red pearls; or an element of your choice. Each player receives four face-up search cards; on a turn; you choose one of those cards and ask an opponent how many gem cards they have of the type shown. If you ask for; say; pairs; the player must tell you how many pairs they hold but not which specific pairs; if you ask for something more specific; say; red diamonds; the player reveals to everyone how many such cards she holds while you get to look at them in secret.
Players track information on a score pad. You can guess the hidden gem at any time; or on your turn you can ask any one question regardless of which search cards you have; then immediately make a guess by marking your sheet and checking the hidden gem card. If you're wrong; you keep playing but can only answer questions; if you're correct; you win.
The simplicity of the rules and the cards belies the complexity of the game. In some cases you see cards; while in others you hear only the number of cards that an opponent holds; making it tough to deduce. Any notation system you devise must be both flexible and reliable; recording negative information as well as positive in order to tick off the possibilities one by one...