Only the Sultan knows what objects
Two or more people can play. One player (or team, if desired) is selected to be Sultan for the first round. The other players are the jewel thieves.
The Sultan privately thinks of a "jewel rule". A jewel rule is simply the description of a set of objects. Some examples of jewel rules are: "round objects", "words containing double letters" , "shapes that can be drawn without lifting the pencil from the paper", or "government agencies". Anything that fits the jewel rule is considered to be a jewel object. Anything else is a sand object.
The Sultan writes the jewel rule on a piece of scratch paper and keeps it hidden. He then writes a jewel object on a blue Post-it and a sand object on a yellow Post-it, and places them both in the DESERT (i.e. the yellow sheet of paper).
The jewel thieves, considering the objects revealed by the Sultan so far, create together a "sieve rule". A sieve rule, like a jewel rule, is simply a description of a set of objects. Although they will not yet know if their sieve rule matches the jewel rule, it should at least be capable of sifting the jewel object(s) from the sand object(s) revealed so far. The jewel thieves move the revealed jewel object (i.e., the blue Post-It) to the SIEVE, leaving the revealed sand object (i.e., the yellow Post-It) in the DESERT.
If the sieve rule proposed by the jewel thieves does not match the jewel rule (i.e., not by its exact wording, but in the objects it selects), the Sultan must prove it by revealing another jewel object that slips through the SIEVE into the DESERT, plus another sand object that is caught by the SIEVE. In other words, the Sultan will place a blue Post-it on the yellow sheet of paper, and a yellow Post-it on the blue sheet of paper.
There are two exceptions. On the one hand, if the sieve rule happens to be a subset of the jewel rule, the SIEVE will let some jewels slip through to the DESERT, but it will not catch any sand objects. In this case, it is not possible for the Sultan to reveal another sand object caught by the SIEVE. On the other hand, if the sieve rule is a superset of the jewel rule, the SIEVE will catch all the jewels, but it will also catch some stray sand objects. In this case, it is not possible for the Sultan to reveal a jewel object that slips through the SIEVE into the DESERT. (The normal case, where it is possible for the Sultan to reveal both objects, is called an intersection)
The jewel thieves now examine the new objects and come up with a new sieve rule to test. If the sieve rule is still not correct, the Sultan uses the same process of revealing new objects to prove it. When the sieve rule is finally correct (or, what amounts to the same thing, the Sultan cannot think of objects to disprove the sieve rule -- even though the sieve rule may be worded differently from the jewel rule), the round is over. The Sultan gets ten points for each jewel object revealed plus one point for each sand object revealed.
The next player becomes the new Sultan and a new round is begun. The game is over when every player has been the Sultan once (or twice, or thrice, etc. for longer games) and the player with the most points wins.
One of the problems I have struggled with in the "read about it on the Web" version is that the Sultan could think of a jewel rule so complicated that no one could ever hope to guess it. If I ever have the opportunity to market the game, the obvious solution would be a set of cards with pre-determined jewel rules for the Sultan to draw from.
Since that marketing possibility may not occur very soon, one solution is to only play with people who enjoy the process of the game. They will thus police themselves to pick reasonable jewel rules and rely on their wits to come up with tricky jewel and sand objects in order to mislead the jewel thieves.
Another variation that overcomes this problem is to play with two teams. One person on each team is a Sultan playing against the other team's jewel thieves. If it is not too confusing, you can even have two games played at the same time, each Sultan having a jewel rule. The Sultans can then examine and proclaim each other's jewel rule as acceptable.
Another interesting addition to this variation (if you can handle the complication) is to have Sultan "A" provide jewel objects for the team "B" jewel thieves, but let Sultan "B" provide the sand objects. In this way, the Sultan "A" tries to give TRICKY jewel objects for the "B" jewel thieves while Sultan "B" (who is on the same team as the "B" jewel thieves, but cannot guess) tries to provide HELPFUL sand objects.
If the jewel rule were, say, "purple objects", Sultan "B" could give it away easily by providing a sand object like "a non-purple bicycle". To prevent this unfair situation, Sultan "A" gets to authorize the sand objects provided by Sultan "B".
Another option in this variation is to allow Sultan "B" to provide up to two sand objects each time with the following conditions: Sultan "B" can already provide a sand object that gets caught by the SIEVE (unless the sieve rule happens to be a subset of the jewel rule -- see above). He can also be allowed to provide another sand object which does not get caught by the SIEVE (he will always be able to do this, no matter if the sieve rule is a subset, superset, or intersection of the jewel rule). The rationale for this option is that it is difficult to provide helpful sand objects (barring the unfair ones mentioned above), so this balances the scales a bit.
It can sometimes help to label the sieve rules "(a)", "(b)", "(c)", etc., in the order they were proposed. Then use this designation on the jewel and sand objects (i.e., the blue and yellow Post-Its) to identify which sieve rule they were added as a result of.
If you try this game out, I would be interested to see the jewel rules used. If you have the energy, I would even be interested in seeing the objects and progression of the game (the a,b,c designation described above would allow me to follow it easily). If I had enough responses, I would like to consider having a page of jewel rules (and even full games) provided by readers of this page.
As always, any comments and suggestions are welcome, particularly suggestions about how to prevent the "impossible to guess jewel rule" fairly.