The Trial's Solution

The Trial:

The King has one of these strange boxes that hides a flower. He can choose to find the smell of the flower, by opening the door on the top of the box, or the color, by opening the door on the bottom of the box. There are two possible outcomes for each measurement, rose-smell or trillium-smell and red or white, respectively. The odd bit comes about when you make repeated measurements of the same property. For instance, if one makes a smell measurement and then a color measurement then, when one measures smell again, it may not be what you started with. However, if you just measure smell, and do not touch the other door, then you will always get the same result.

So, the King requires that you find out (with measurements or more sophisticated operations) the results of his measurement - both which door he opened and what he found. You are only allowed to perform operations on his box before and after the King's measurement.

A Solution:

One method is to use another box. Entangle the King's box with your box so that a smell measurement will give a sweet, wild rose smell if the King decides to measure the flower's smell and a trillium odor if the King decides to measure the flower's color. After the King makes a measurement, you make a smell measurement on your box. If the smell is of rose then the King measured smell and you can use his box to determine it. If your box does not smell of rose, by the correlation that you set up, you are certain that the King measured color. You can then measure color of his box knowing that it has not been scrambled.

So the next time you meet a king of this sour disposition (and I remind you that you have now thought about physics) you can pass this test with flying colors.