When Carl Friedrich Gauss was just a schoolboy, he surprised his teacher by solving a seemingly tedious task—
adding all numbers from 1 to 100—in a matter of seconds. He noticed a clever pattern: pairing numbers from opposite ends of the list always gives the same result.
This insight is now known as Gauss's Method.
The General Idea
To sum the first n natural numbers:
1 + 2 + 3 + … + n = n(n + 1)/2
To sum an arithmetic progression with first term a, last term l, and number of terms n:
Sum = n(a + l)/2
This method works for both simple sequences (like 1 + 2 + 3 + …) and more general arithmetic progressions
(like 3 + 6 + 9 + …).
Problems
Find the sum of all natural numbers from 1 to 50.
Find the sum of all odd numbers from 1 to 100.
Find the sum: 1 + 2 + 3 + … + 100.
Find the sum: 3 + 4 + 5 + … + 49.
Find the sum of all two-digit numbers.
Find the sum of all four-digit numbers.
Find the sum of all natural numbers from 1 to 150 that are divisible by 3.
Is the sum 1 + 2 + 3 + … + 2025 divisible by 2025?
Find the sum of all natural numbers greater than 80 and divisible by 6, with remainder 1.
The sum of five consecutive natural numbers is 1115. What are these numbers?
The sum of six different natural numbers is 22. What are they?
Ten fishermen caught 25 fish with masses 100 g, 200 g, ..., 2500 g. How can the fish be fairly distributed so each fisherman gets the same total mass?
How many two-digit numbers have the first digit greater than the second?
Digits 1 to 9 are arranged in a circle. Any three consecutive digits form a three-digit number when read clockwise.
Find the sum of all such three-digit numbers. Does the result depend on the arrangement?
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
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