Metashkola Olimpiada Po Matematike Zadaniia <AUTHENTIC × TUTORIAL>

Focus on topics like combinatorics , Dirichlet's principle , and geometric transformations .

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

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. Focus on topics like combinatorics , Dirichlet's principle

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? Preparation Resources To prepare for the official rounds,

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)