# A Mathematician’s Guide to Arranging a Seating Plan

#### Mathematical table numbering

Maths is full of the flourishes of the ancient Greek alphabet – such as λ (lambda), φ (phi) , θ (theta), α (alpha), β (beta) – as well as the mystery of special mathematical numbers, such as ∞ (infinity), π (pi), e (Euler’s constant) and i (imaginary number). This couple designed some excellent mathematical challenges for guests, based on their table number.

Instead of numbering your tables 1, 2, 3, 4, 5… why not ring the changes and use some mathematical patterns, such as:

**1, 2, 3, 5, 8, 13, 21, 34, …**This is the Fibonacci sequence and is found in lots of natural things, from the number of petals on flowers to the patterns of a family tree.**1, 4, 9, 16, 25, 36, …**square numbers (1×1, 2×2, 3×3, 4×4, 5×5)**2, 3, 5, 7, 11, 13, …**prime numbers

Offer a prize to whichever guest works out the pattern you have used first!

#### Maths challenge seating plans

Challenge your guests to solve mathematical puzzles in order to find their table! You can do easy sums like “9 – 1” to help children find table 8, or complicated stuff like “4! – 4²” to tell a mathematically minded adult they are sitting at the same table. This seating plan is a great example of a maths challenge seating plan.#### Table décor for the mathematician

Table layouts can also be mathematical. Include spirals or symmetry, or search out mathematically themed décor, such as this great ruler table runner.

#### How do the real mathematicians do it?

There are a number of mathematical ways to model a seating plan. The ‘menage problem‘ models a seating plan where genders alternate and couples don’t sit together. You could turn your hand to computer programming to find a solution – this article (see section 3.3) explains how you can use Python code to create a seating plan which minimises a guest’s unhappiness at being seated with someone they do not know or like.

However, our favourite has to be this mathematical optimization model created by Megan Bellows and Jean Luc Peterson, of Princeton University, for their wedding. They wanted to make sure as many friends were sat together as possible, so used a ‘connection matrix’ to weight the strength of the friendship between each pair of guests.

The couple invited 107 guests to their wedding, and wanted to seat them on 11 tables seating 10 people each. It took **over 36 hours** to find an optimal solution for the couple’s wedding seating plan and, even then, it needed some last minute adjustments from the groom’s mother!

#### Does TopTablePlanner use all that complicated maths?

The simple answer is no. A mathematical model and rule based approach can work really well in some situations. However, for the vast majority of events by the time all the ‘rules’ have been entered and the inevitable manual tweaks have been done at the end, it’s far simpler and quicker to arrange guests manually!