Problems

1. Divide {1, 2, 9, 25, 49, 64} into two subsets so that the sum of the numbers of one of them is equal to the sum of the numbers of the other.

2. Anya and Tanya together weigh 40 kg, Tanya and Manya - 50 kg, Manya and Vanya - 90 kg, Vanya and Danya - 100 kg, Danya and Anya - 60 kg. How much does Anya weigh?

3.
a) Four merchants noticed that if they join without the first, they will collect 90 rubles, without the second - 85, without the third - 80, without the fourth - 75 rubles. How much money does anyone have?

b) Solve the system of equations: y + z + t = 90, x + z + t = 85, x + y + t = 80, x + y + z = 75.

4. The average age of the 11 players on the football team is 22 years old. During the match, one player was injured and left the field. The average age of the remaining players is 21 years old. How old is the person injured?

5. The teacher conducts a lesson in the classroom. The teacher's age is 24 years older than the average age of the students and 22 years older than the average age of everyone present in the class. How many students are there in the class?

6. Kate, Lena, Michael, Kristina took part in the concert. Each song was sung by 3 girls. Kate sang 8 songs - the most; Kristina has the least number of songs - 5 songs. How many songs were sung?

7. Is it possible to write the natural numbers from 1 to 30 in a table of 5 rows and 6 columns so that all six sums of the numbers in the columns are equal?

8. Is it possible to fill a table of size

a) 5×5 with numbers?

b) 6×6 so that the product of all numbers in any row is negative, and the product of all numbers in any column is positive?

c) Is it possible to arrange the numbers in a 19×66 table so that the sum of the numbers in each row is positive, and in each column the sum is negative?

Where do you hold your classes?

We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London.
You can find our timetable here.

What do you need to start learning online?

For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.

When can I take the trial lesson?

You can get acquainted with the school at any time convenient for you. To do this, just leave a request and sign up for a lesson.

What should I expect from the trial lesson?

The trial lesson is a 30-minute online session designed to get a sense of how your child approaches mathematical thinking and problem solving. (In practice, it often runs a bit longer if the student is engaged!)

We typically explore a range of fun and challenging problems drawn from competitions. We adapt the difficulty based on how the student responds, aiming to make it both accessible and stimulating.

After the session, we’ll have a quick conversation with the parent to share observations and suggest a personalised path forward.

I can't attend class, what should I do?

It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to

I don't have much free time, will I have time to study?

Learning can take place at your own pace. We will select a convenient schedule and at any time we will help you change the schedule, take a break or adjust the program.

How long is one lesson?

All classes last 1 hour.

Meet our team

Our teachers will tell you how to prepare for exams, help you cope with difficult tasks and win the Olympiad
‍
They will tell you about the pitfalls of exams and the most common mistakes, and explain how to avoid them

George Ionitsa

Founder &
Maths and Coding Coach

Hear from some of our amazing students who already achieved incredible results with us!

"Olympiad Maths Lessons helped me a lot to get the Gold medal in Junior Maths Challenge"

St. Paul's Student

"Thanks to the 'Data Science' and 'Coding in Python' lessons I got accepted to my dream university."

Data Science Student
Warwick University

"Great courses, which thoroughly explained topics beyond the capability of the GCSE answer sheet. Thanks so much."

Ivan

GCSE Student in Dubai

"Financial Mathematics! Best course to understand Python and Mathematics behind Finance!"

Gleb

VC Investor

"We got silver in PMC! Thanks George!"

Mum of St. Paul's Student

Prepare for the Primary Maths Challenge

"My daughter took a batch of 10 classes with George to understand Python with Turtle. I found George extremely knowledgeable and accessible."

Dad of Latymer School Student

Python with Turtle