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?

What is the next number in the pattern? Explain the rule used.

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)

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:

Below is a draft of a sample paper structured similarly to a mid-level MetaShkola competition (suitable for grades 5–7). Time Allowed: 60 minutes Total Points: 100 Part 1: Logical Reasoning (5 points each)

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?

A rectangle is divided into three identical smaller rectangles, each with a perimeter of 20 cm. What is the perimeter of the original large rectangle?.

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.

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