Back in 1963, Robert Abbott developed the game "What's That on My Head?". He now runs the excellent site logicmazes.com and frequently appears in Games Magazine, so he's still active in recreational logic.
In this updated version, there are 28 tiles.
There is 1 1, 2 2s, 3 3s, ..., and 7 7s. There are also 4 of each shape.
Grn Oval - 1 6 6 6
Ylw Tria - 2 2 7 7
Nvy Star - 3 3 3 5
Brwn Box - 4 4 4 4
Orgn Hex - 5 5 5 5
Red X - 6 6 6 7
Cyan Dmd - 7 7 7 7
Each person gets 3 tiles, but you cannot see your own tiles. You can see everyone else's tiles, and some tiles remain unknown. Each turn, a player asks another player a question via one of 23 question cards.
1. How many colors/shapes can you see?
2. On how many racks is the sum of the numbers 12 or more?
3. On how many racks do you see only even or uneven numbers?
Based on their answer, you can some sort of deduction about your tiles. For example, if the answerer said 1 rack to question 3, and you saw none, you could deduce that your rack had all even or uneven numbers.
Later in the game, you can start making deductions based on people not making deductions. "If my tiles were 1 2 3, then Bob would have been able to easily deduce his own rack based on the questions so far. Since he hasn't, I cannot have 1 2 3." Of course, that can get hairy. At level 1 are simple deductions. Assuming everyone has done level 1 allows level 2 deductions.
Highly durable domino-material tiles and racks. This is a high-quality game.
Recommended.