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) metashkola olimpiada po matematike zadaniia

The MetaShkola website (Russian language) provides past problems and solutions. At a math circle meeting, 10 students met

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? One always tells the truth, one always lies,

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)

Find the smallest natural number whose digits sum to 25 and which consists only of different digits. Sequence Logic: Look at the sequence: