Christmas encourages us to do nice things for others: go grocery shopping for the elderly neighbour, donate to one of many charities, or even smile to a stranger. Unfortunately, it might get a bit frustrating, because all these good deeds seem so insignificant. In the end, how much can one person achieve? Of course, maths will help us answer this question. Let’s say on December 1 you help just two people. On the December 2, inspired by your niceness, each of them helps two other people. The next day each of them helps two other people, and so on, until Christmas. How many people will this chai ..read more

Santa Claus is comin’ to town… But first his elves have a huge task ahead of them: determine which kids behaved well this year, go through their letters to understand what gift they want and finally wrap the presents. Despite appearances, Santa is a talented entrepreneur. “Time is precious,” he often remarks, “so we have to improve our efficiency.” Elves from the Department of Mathematics and Statistics at the University of North Pole analysed the average time the team spends on different tasks. They found that for each child the whole process takes seconds, of which the elves need for admin ..read more

One of the most beautiful Polish Christmas Eve traditions is leaving an empty chair for an unexpected visitor. We believe that nobody should be alone for Christmas, so we’re ready to welcome anyone who’d like to join us (not sure how it will work during 2020 pandemic though). Soon after Bolek and Lolek, two flatmates, sat down to their Christmas dinner, they heard a knock on the door. “Are we expecting anyone?” Bolek asked. “Maybe it’s Santa!” Lolek responded, only half-jokingly. “I’ll go and check.” It wasn’t Santa, but their neighbour Tola, who felt lonely this Christmas Eve. Following the t ..read more

As a child, I always wanted to know how many Christmas gifts my friends received. I strongly believed that the number of presents brought by Santa Claus was directly proportional to our behaviour during the year, so I wanted to judge how well-behaved I was in comparison to other kids. I couldn’t have been as naughty as my parents claimed! However, my family repeatedly told me that asking such questions could be rude—so I never learned if Santa ranked me lower or higher than an average child. Only years later did I find a solution. If you have similar doubts, read on! Let’s say Harry, Ron and H ..read more

Marco and Robi both considered themselves masters of gifting. “Everyone’s always happy with my presents,” Marco claimed. “Wanna bet my gifts are more successful than yours?” Robi suggested. “Deal! Let’s count how many people are satisfied with our Christmas presents.” Both boys are scientists, so they diligently approached the process of gathering data. After Christmas, Marco rejoiced his victory. “Told ya! We both gave presents to ten people and five of my gifts made someone happy, while only four of yours,” he rubbed it in. “Not so fast, my dear brother,” Robi protested. “I’m sure you’ll agr ..read more

Each December Varsovians wait impatiently for the Christmas illumination. Every year the decorations are different, so I’m always excited to discover what our artists came up with. Luckily, the pandemic didn’t change at least this aspect of Christmas. Of course, the most important part of Christmas illumination is the tree. This year, according to the City of Warsaw, it’s 27 m tall. But is it decorated properly? Warsaw Christmas tree in 2020. Beautiful, isn’t it? Thanks to the members of Sheffield University Maths Society (SUMS), we have formuale for the perfect length of the tinsel and lights ..read more

Little Monty can’t wait to open his Christmas present! He gets even more excited when he sees his mum bringing not one, but three boxes wrapped in a festive paper. “One box contains the toy car you asked for,” says Mum, “and in the other two you’ll find apples. Pick your present carefully!” Monty suddenly feels responsible for his present. It means he’s basically an adult! But how to choose the right box… In the end, he points at the gift in the middle. “Are you sure?” asks Mum. “To help you with your decision, I’ll show you where one of the apples is. Afterwards, you can still change your min ..read more

You packed 9 identical presents and started labelling them, when you remembered that in fact only 8 are identical: one of them is the special gift for the special person. You don’t have more wrapping paper, so you don’t want to unpack them, but you need to identify the special present! You know that the box you’re looking for is slightly heavier than the rest. The only scale you have at home is an old-fashioned balance scale. Unfortunately, it belongs to your grumpy uncle, who’s so afraid you’ll destroy his favourite item that he lets you use it only 2 times. How can you identify the special g ..read more

We usually don’t think twice about getting Christmas gifts for closest family members and friends. But what about the not-so-close friend you’re going to see around Christmas (in a socially distanced way, of course!)? Should you even bother? Luckily, the branch of mathematics called game theory offers us some answers. You just need to attach numerical values to the benefit of receiving a gift (which includes both the material and emotional component) and the cost of giving (again, combining the money and effort). Let’s say that the benefit of receiving a present is and the cost of giving a pr ..read more

Do you want to give everyone a Christmas gift without breaking the bank? Secret Santa is your friend! I, Mum and Dad put pieces of paper in a hat, with one letter each: P for Paula, M for Mum and D for Dad. We draw these letters at random and the resulting letter represents the person we’ll buy the gift for. Mum starts, followed by Dad and me. Nobody should buy presents for themselves, so if Mum draws M or Dad draws D, they put letters back inside and draw again until they pick a different letter. It’s more problematic if I end up with P, because no letters are left to exchange it for–so we h ..read more