## Posts Tagged ‘**mathematical puzzles**’

## Adventures in the Counterintuitive…

Your correspondent is headed away for a week or so, ranging more then ten times zones from home– the current limit to continuous timely posting of (R)D… So, while regular service will resume on-or-around the 20th, a little something to keep one occupied:

Readers will recall that, on the occasion of an earlier hiatus, your correspondent wheeled out “the Monty Hall Problem” (c.f., “**Riddle Me This**” and “**Birdbrains**“). This time, with thanks to **Prof. Stan Wagon** at Macalester College:

Alice and Bob face three doors marked 1, 2, 3. Behind the doors are placed, randomly, a car, a key, and a goat. The couple wins the car if Bob finds the car and Alice finds the key.

First Bob (with Alice removed from the scene) will open a door; if the car is not behind it he can open a second door. If he fails to find the car, they lose. If he does find the car, then all doors are closed and Alice gets to open a door in the hope of finding the key and, if not, trying again with a second door.

Alice and Bob do not communicate except to make a plan beforehand. What is their best strategy?

Source: A. S. Landsberg (Physics, Claremont Colleges, California), Letters, Spring 2009 issue of

The Mathematical Intelligencer.

The answer is **here**— and more nifty puzzles, **here**.

**As we craft our own strategies,** we might solve a memorial problem for Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, the French mathematician and physicist who is probably better known as Voltaire’s mistress; she died on this date in 1749. Fascinated by the work of Newton and Leibniz, she dressed as a man to frequent the cafes where the scientific discussions of the time were held. Her major work was a translation of Newton’s *Principia*, for which Voltaire wrote the preface. The work was published a decade after her death, and was for many years the only translation of the *Principia* into French.

Judge me for my own merits, or lack of them, but do not look upon me as a mere appendage to this great general or that great scholar, this star that shines at the court of France or that famed author. I am in my own right a whole person, responsible to myself alone for all that I am, all that I say, all that I do. it may be that there are metaphysicians and philosophers whose learning is greater than mine, although I have not met them. Yet, they are but frail humans, too, and have their faults; so, when I add the sum total of my graces, I confess I am inferior to no one.

– Mme du Châtelet to Frederick the Great of Prussia

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