pseudonym/mathematics

Fascinating videos on dimensions.

See the powerful implications of exponential growth.

Mental mathematics performed in lightning style.

From the page: "Still, because of the ambiguity in the wording, it is impossible to solve the problem as stated through mathematical reasoning. The strict argument, Dr. Diaconis said, would be that the question cannot be answered without knowing the motivation of the host.

Which means, of course, that the only person who can answer this version of the Monty Hall Problem is Monty Hall himself. Here is what should be the last word on the subject:

If the host is required to open a door all the time and offer you a switch, then you should take the switch, he said. But if he has the choice whether to allow a switch or not, beware. Caveat emptor. It all depends on his mood.

My only advice is, if you can get me to offer you $5,000 not to open the door, take the money and go home."

Some sage advice indeed from the old pro himself: "Take the money and go home!" :-)