If you’re a teacher, you can find my similar annual course in eBook format on Amazon (If you have an eBook Amazon subscription, you can access it for free). Please feel free to reach out to me, and I would be delighted to send you the entire course, complete with keys and answers, in PDF format. If you’re interested in collaboration, I’m open to customizing the course according to your students’ needs. I’ve compiled a substantial collection of unconventional Olympiad problems for 8th to 11th graders and would be happy to share them. Respectfully, Mark.
At the heart of the Olympiad Math Club lies a vibrant community dedicated to exploring and mastering mathematical challenges. We are open to a wide spectrum of young enthusiasts—from those taking their first steps to experienced problem-solvers seeking to explore their skills.
Our Approach - We believe in learning through doing. Thus, our curriculum, spread across an annual course, is crafted to encourage active participation and self-paced progression. The problems are collected from esteemed math sources focused on preparation for math Olympiads and contests, ensuring that our members engage with only the finest materials.
Course Structure - The course is thoughtfully segmented into weekly modules, featuring two distinct categories of problems: Warmup: These are problems designed to be tackled more easily, serving as a perfect starting point for beginners and a quick exercise for the experienced. Advanced: For those craving a deeper challenge, our advanced problems offer a rigorous workout for the mind.
Weekly Modules: Dear Readers, in this section, you will always find 6 latest Modules available to you. Each Module comprises 12 math problems sourced directly from actual Math Olympiads. In fact, each Module can be viewed as a mini math contest, tailor-made for Middle and High school. Please note that every Module should take 1 week to solve, and its answer keys will be shared via Google Messenger once the week is over on Friday.
1.1 There are buses driving around a circular route. They are located at an equal distance from each other. There are 2 buses, and they run at 15-minute intervals. The question: If we add another bus, what will the new interval be? Note that the buses always drive at the same speed.
1.2 The kangaroo can jump either 6 m or 8 m along a straight line. The question is whether the kangaroo can reach a point at a certain distance from the starting point. The distances: a) 1.5m b) 7m c) 4m.
1.3 George put bolts in one box, screws in another box, and nuts in a third. He labeled each box, but unfortunately, all the labels got mixed up — none of them matches the actual contents. Now, your task is to figure out, by opening just one box, where each type of hardware (bolts, screws, and nuts) is located.
1.4 Andrew loves weighing his toys on a scale! He found that one ball and two blocks balanced a car on the scale. Two balls balanced a car with one block on the scale. How many blocks by themselves would it take to balance the car? Remember: All the blocks weigh the same, and all the balls weigh the same!
1.5 Billy has 7 potatoes. Peter has 5 potatoes. Joe has no potatoes. The boys cook the potatoes and divide them equally between one another. In turn, Joe, grateful because the boys shared their potatoes with him, gives Billy and Peter 12 candies. The question: How should Billy and Peter divide the candies fairly between each other?
1.6 Imagine you’re taking shots at a target (on the right), trying to score exactly 100 points. To solve this, let’s think about how we can combine different scores to reach 100 points.
2.1 5 cats ate 5 sausages in 5 minutes. How many sausages will 10 cats eat in 10 minutes? ᓚᘏᗢ
2.2 The cards are numbered 415, 43, 7, 8, 74, 3. Arrange the cards in a row so that the resulting ten-digit number is the smallest possible.
2.3 75 books were put on two shelves, and the first shelf has 13 books less than the second shelf. How many books are on each shelf ?
2.4 Is it possible to write 9 natural numbers in a circle so that the sum of any two adjacent (neighbor) numbers is odd?
2.5 The pet shop sells big and small birds. A big bird costs twice as much as a small one. One boy bought 5 big birds and 3 small ones, and another boy bought 5 small birds and 3 big ones. The first boy paid 20 dollars more. How much does each bird cost? Alice and Peter did not want to use the elevator on the first floor and decided to go up to their apartments by stairs. Alice lives on the 3rd floor, and as she climbed the stairs, she counted 36 steps. How many steps will Peter count to his apartment if he lives on the 9th floor?
2.6 Alice and Peter did not want to use the elevator on the first floor and decided to go up to their apartments by stairs. Alice lives on the 3rd floor, and as she climbed the stairs, she counted 36 steps. How many steps will Peter count to his apartment if he lives on the 9th floor?