When you are sitting around the table on Christmas Day, wondering what to talk to your Great Uncle Norman about, a few mathematical curiosities can be just the thing to keep the conversation lively. Christmas is full of patterns, puzzles and surprising numbers, and sharing a few of them might even earn you the title of “most interesting guest at lunch”.

One of the most famous examples comes from the song The Twelve Days of Christmas. While it sounds like 12 gifts are given, the total is actually much higher. Because each day includes all the gifts from the previous verses, the numbers stack up in a triangular pattern. When you add them together, the final total reaches 364 gifts which is almost one for every day of the year. It is a lovely reminder that repetition in music often hides beautiful mathematical structure.

If you find yourself admiring the Christmas lights, there is a neat bit of number magic hidden in the blinking patterns. Two sets of flashing lights might look random, but the timing of their flashes can be explained using the least common multiple. For example, if one set repeats its pattern every 5 seconds and another every 8 seconds, they will line up perfectly every 40 seconds. Understanding this little trick turns a simple decoration into a miniature maths demonstration.

Snowflakes also offer a wonderful chance to appreciate geometry in nature. Each real snowflake forms with six-fold rotational symmetry, which means you can rotate it by 60 degrees and it still looks the same. This repeating structure occurs because of the way water molecules naturally arrange themselves as they freeze. Even though no two snowflakes are identical, they all share this elegant six-pointed design at the heart of their formation.

Christmas crackers add another opportunity for a bit of fun mathematical thinking. When everyone pulls a cracker with the person next to them, the outcome of each pull is like a tiny probability experiment. If eight people are pulling at once, each with two possible results, the chance that everyone ends up winning their cracker is only 1 in 256. It is unlikely, but that is what makes it such an entertaining example to share around the table.

Decorating the tree can also be a surprisingly mathematical exercise. If you have ten unique baubles and decide to hang them in different orders, there are 3,628,800 possible arrangements. This huge number comes from factorials, which multiply each number by every number below it. So if someone suggests your arrangement is unusual, you can happily explain that you are simply exploring one of the many creative possibilities.

As we head into the Christmas season, I wish everyone a safe, joyful and peaceful holiday filled with warmth and laughter. This will be my final newsletter article as Maths Learning Leader, and it has been a genuine pleasure serving in this role for the past five years. Thank you for your support, your enthusiasm and the many wonderful moments shared along the way.

Dr Karen McMullen

Learning Leader: Mathematics