# How I made family dining 40,320 times better

Some people have a favorite color or flower. I have a favorite math problem: How many ways can eight people be seated around a dinner table? My daughter came across the question several years ago in a junior high math assignment. Its mind-boggling answer (40,320) affirmed my instinctive refusal to let my kids choose a new place at the table each meal. My family of eight could wrangle over who sits where (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320) every night of the week (40,320 x 365 days) for 110.46 years before exhausting the possible configurations.

Nineteen years ago, when my husband and I plunked ourselves down for newlywed meals, we failed to fully appreciate the 2 x 1 = 2 possibilities for arrangement. Nor did we calculate how the growth in seating options would rise (exponentially, inversely proportionate to the narrowing of elbow room) as subsequent offspring graduated from highchair to table. Our first child gave our family six seating possibilities. The second expanded our choices to 4! (the symbolic way to express 4 x 3 x 2 x 1 = 24, verbalized as "four factorial"). The third gave us 120, and the fourth 720, before twins sky-rocketed our options to the 40,000 number that inspires my sit-in-your-own-seat theorem.

When I was growing up, there were only seven of us, which meant a mere 5,040 ways to arrange the family at dinner. But even 7! was more plate shuffling than my mother was willing to quantify. We had assigned seats. My mother sat closest to the refrigerator, my father by the phone. As middle child, I was sandwiched between siblings at the far end of the table, my back to the wall. From this vantage I could survey the entire kitchen, and once wedged in for the meal I was virtually never asked to get up and get somebody another fork or more sour cream. I loved my place.

My own children feel similar possessive dominion over their suppertime seats, which makes impromptu resituating impossible. One child might, on a night of daring, try sitting at another's place. A second child, feeling game, might then slide nonchalantly onto a different chair. Such casual repositioning can ripple smoothly through four or even five children, until the last little bear arrives and cries: "Somebody's sitting in my chair!"

"Well somebody's sitting in my chair!" The chorus reverberates through the kitchen until Mamma Bear roars: "SIT IN YOUR OWN CHAIRS!"

We then begin our lovely meal.

Last week while wiping down the table, I discovered another advantage to knowing who sits where. Under the edge of the tabletop, I came upon a filigree of scratches and nicks embellishing the foot-long stretch where teenage Max sits. From the juvenile looks of his signature "M," I dated the inception of this project to the mid-1990s; wood dust on a fresh gouge led me to believe the work was still in progress. Inching along, I found a row of chicken scratches at the 8-year-old's place as well, evidence of an apprenticeship. It would seem a mealtime wood-carving renaissance has blossomed while I've been obliviously passing the peas.

Discovering my children's under-the-table shenanigans reminded me of how years ago my own mother used assigned seating to solve the Mystery of the Cascading Bread Crusts. For company meals, the leaves of our dining table slid out from along a track under the tabletop. Once, my wandering fingers discovered that this track provided a handy shelf for disposing of unwanted bread crusts and lima beans. I thereby cleaned my plate, which pleased my mother. That is, until the table was slid back into place and my stockpile tumbled to the floor. It was, you could say, an open and shut case: I always sat there.

And now, in my own home, I sit at the east end, closest to the refrigerator. It is a choice arrived at by mathematical calculation: If eight people can be arranged around a table in 40,320 configurations, how many ways can these same eight argue over who should jump up and get more sour cream?

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