A three-digit number is divisible by 9. If you swap the first and last digits, the new number is also divisible by 9. How many such numbers exist where the middle digit is 5? Part 3: Geometry & Spatial Thinking (15 points each)
Platforms like YouTube offer walkthroughs for similar Russian-style olympiad problems.
You have 9 identical-looking coins, but one is slightly lighter than the rest. Using a balance scale, what is the minimum number of weighings needed to guarantee finding the fake coin? Preparation Resources To prepare for the official rounds, students often use: metashkola olimpiada po matematike zadaniia
At a math circle meeting, 10 students met. If every student shook hands with every other student exactly once, how many handshakes were there in total?
Three people (A, B, and C) are in a room. One always tells the truth, one always lies, and one can do both. A says: "I am the truth-teller." B says: "A is the liar." C says: "I am the one who can do both."Identify who is who. Part 2: Number Theory & Arithmetic (10 points each) A three-digit number is divisible by 9
A farmer needs to transport a wolf, a goat, and a cabbage across a river in a boat that can only hold himself and one other item. If left alone, the wolf eats the goat, and the goat eats the cabbage. How many trips across the river are required to get everyone safely to the other side?
The mathematical olympiad is a popular online competition in Russia designed to challenge students' logical thinking and non-standard problem-solving abilities. Unlike typical school exams, these tasks often require a creative approach rather than just formulaic calculation. Part 3: Geometry & Spatial Thinking (15 points
The MetaShkola website (Russian language) provides past problems and solutions.