The Curve of Baguette Freshness and Other of O-la-la Moments.

This August we were lucky to spend a few weeks traveling around France: first we explored Paris, and then drove South to the magnificent Loire and Dordogne river valleys.  Below are some math vignettes from our adventures. Feel free to post your thoughts to either  the mathematical or non-mathematical musings in the comment section below.


This trip consolidated my opinion that Paris is the most beautiful city I have ever visited, with the worst food I have tried.  I know, many of you will disagree with either statement, but hopefully not with both. Don't get angry, this is just my personal opinion.  I have been in Paris before but I have forgotten the magnificence of its museums and churches gracefully situated along the Seine, the elegance of the Gothic architecture, the beauty of the city gardens, the gentle curves of window rails that differ from building to building,  the rich history you can google and visualize on every street, and the ingenuity of the modern buildings on La Defence.

Image by Tallapragada, distributed under CCL.

Before we left for France I idealized the baguette for my kids, promising them daily bakery shopping and picnics on the grass.  But we all quickly learned the delicate lifespan of this symbol. Following is a graph of baguette freshness.

Baguette is at its best around 6am when it is just baked. It is still a bit warm around 8am when you buy it and steal a generous piece. It is cold, chewy on the outside but soft inside when you eat a sandwich with it around noon. By the time it is being served for dinner in a breadbasket it is a jawbreaker.


In one of the attempts to eat something other than baguettes or crepes, following an advice of a local, we ventured into the Chartier restaurant on Montmartre street.  Great atmosphere of a busy old train station, good and inexpensive food that, as everywhere in France, lacks fruits and vegetables. And of course, coffee with dessert, which brings us to math.  In our party, two people ordered decaf and one a real coffee. The waiter brought a large plate with three small identical cups on it. To my question which one is the caffeinated he reluctantly pointed to one and quickly retreated.  There was absolutely nothing on the plate to distinguish this cup from the other two, it looked like a joke but we were far from laughing as one of us needed caffeine for driving and two others were looking forward to a good night sleep. What do you think were the chances that the cup I picked was really a decaf?


Serendipitously I discovered a great way to make our kids spend half-a-day in the Louvre and think it is fun!  Daisy de Plume, New York expat living in Paris, with a background in art history and tremendous knowledge, created a series of Treasure Hunts that you can do at the Louvre.  Ours was "The Best of Biestery" and we scanned half of the museum in 3 hours looking for the paintings, sculptures and vases that Daisy described. The proof that we found each was a family snapshot in front of it.  If you are heading to Paris, check out Daisy's webpage, ThatLou, for more details. Beware that it is for adults and older kids ages 10 and up. Our team won, largely because we had one local on it who had been at the Louvre in the past and I did some homework scanning through Daisy's blog for hints on the treasures she likes and memorizing few room numbers (all following her suggestion).

Our local friend introduced us to a simple and captivating card game. Type of a game that you wish you created yourself. It is called Dobble in French. There is a set of cards where each card has 8 objects on it and every two cards have one and only one object in common.  An object may change its size but not the color. There are few options to play this game but the simplest one is to divide the cards between players, living one at the center as the starter. On a count all the players flip their top card and carefully but frantically compare the card in their hand to the card in the center trying to name an object that is common.  The person who does it first places her card on top of the center card, flips the next card in her pile and the game continues. First to get rid of all of his/her cards is the winner.


How many cards are there overall? We noticed a peculiar detail, that when you divide the cards between two players there is one card left, and when divide between three - there is one left again.
After you figured out how many cards there are, can you count how many objects are there overall if every two cards have only one object in common?

When we borrowed our friend's car to drive down South to the Loire and Dordogne valleys, he warned us of extensive automatic speed ticketing on the French highways.  Apparently you can get a ticket even if the difference between time stamps of entering and exiting a paid highway is less than the shortest possible time you can legally drive between  these points. This sounds simple but we noticed that various road segments have different speed limits. How do you think French police calculates the shortest time?