Combinatorics and Dracula's ‘Smart’ Castle

Senior STEM Camp for Years 3 to 12

24-28 October 2022: Face to Face at Baden-Powell House, SW7 5JS, London


In this spooky Halloween season camp participants will study cryptography where we can hide a secret behind countless possibilities - just one of the many facets of the world of Combinatorics - the mathematical subject at the heart of this camp.

Pupils will also study electronics and programming as they each build their own ‘Smart Castle’ - a model building that reacts to unwanted visitors through programmed sensors! Pupils will be able to take their projects home to demonstrate how they operate and what they have learned. 

All our camps are underpinned by the study and understanding of Maths and Programming. In programming, whether your child is already a confident coder or just starting out, we will create the most appropriate small study group for them, based on their age and experience.

Our pupil to teacher ratio of six to one ensures pupils make good progress and don’t get ‘stuck’. Each group of participants is taught in their own separate classroom to maximise their learning opportunity. Children regularly change classroom, teacher and subject during the day to make sure they are fresh and engaged.

In Electronics, Robotics and Programming, younger participants aged up to 11 years will learn about electronic circuitry as they build a ‘Smart Castle’ to be a Halloween decoration! 

Pupils will learn about electrical safety before creating the electronic circuit needed to provide coloured illuminations for their castle. The castle will even have a steam generator to produce spooky smoke. Once complete, pupils will be able to take the castle home with them to demonstrate what they have learned and achieved.

Older pupils, aged 12 and over, will learn programming and electronics through their practical project of building a more advanced ‘Smart Castle’ for Count Dracula. 

The castle is a model building that pupils will equip with a programmed ultrasonic sensor, LED lights and a steam generator. These features will be controlled by an Arduino compatible microchip that pupils will programme in the Arduino C programming language. The microchip receives information from the ultrasonic sensor that pupils will fit so the castle reacts to unwanted visitors with various coloured lights and spooky ‘smoke’. The ‘smoke’ is created by an on board steam generator. 

Pupils will make the mechanical assembly of the castle and its electronic circuit and learn the programming theory that makes it work. Once complete, pupils will be able to take the castle home with them to demonstrate what they have learned and achieved.


Our focus in Maths this camp will be Combinatorics. How many ways can words be created from a set of letters? How many ways are there to shuffle a pack of cards and in how many cases can a card player be dealt a strong hand? These types of questions are not only important in playing and in gambling but also in cryptography where we want to hide a secret behind countless possibilities. Modern physics provides an even more significant role to this topic. It turns out that a particle can be better described by considering all the possible states it could be in rather than choosing a particular state.

Thus Combinatorics is essential in probability, cryptography, statistics, statistical thermodynamics and quantum-mechanics but also has its own beauty and all the wonderful questions that relate to it.

During this camp pupils will learn how to collect cases in a clever order, how to make a tree diagram and use lexicographic ordering. Children will study how to create formulae based on experience and data and how to find analogous problems and use an earlier result when tackling a new question. Pupils may even have to set up recursions to handle complex tasks and will definitely meet Pascal’s triangle and will discover and apply the secrets of it.

Combinatorics opens the world: instead of sticking to one single result students are challenged to find all possibilities. A useful skill in life.

By year groups, participants will study:

Years 3-6 

Pupils will learn to enumerate all possible cases in a systematic way using lists, tables and graphs. By noticing some patterns in the process and in the arising lists, they will find potential shortcuts that lead to basic combinatorial formulas. Recognizing the situations for direct application of these formulas in various contexts will help deeper understanding of the main ideas of combinatorics.

Years 7-9 

Problems and variations: how to plan, how to structure your work to cover all possibilities. From special to general: making a formula. Number of orderings with conditions.

Different questions with the same answers - what is the underlying mathematical essence? Go deep to get high. Deductive and Inductive formulae.

Years 10-12 

Pascal’s triangle, its variations and tricky applications. Permutations, Combinations and Variations. When deductive formulas are hard to find; how to find and handle recursions.

In our optional Problem Solving Maths sessions from 9.00 to 10.00 each day, participants will study as follows: 

Years 3-6: pupils will be offered challenging problems from UK and international maths contests suitable for their age. 

Years 7-9: ordering numbers, games. Problems with more than one solution. Questions in Probability and Algebra related to Combinatorics. Counting by considering symmetries. Tricky questions about Permutations. Games.

Years 10-12: questions in Probability, Algebra, Number Theory related to Combinatorics. Counting by considering symmetries. The Mathematics of Permutations and games related to it.


Format and fees for the senior face to face camp:

  • pupil to teacher ratio of 6:1
  • participants are taught in small groups, tailored by similarity of age and ability, in individual classrooms
  • camp times: 10am to 3pm
  • or from 9am for an extra hour of problem solving and/or from 3pm to 4pm with our chess class. There is a supplement of £25 for each additional session booked
  • fees are £595 for five days. It is not possible to join for a shorter period 
Places are limited, please register your interest HERE.