This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 3

2017 Bosnia And Herzegovina - Regional Olympiad, 2
Tags: perfect square , arranging , number theory , combinatorics
Prove that numbers $1,2,...,16$ can be divided in sequence such that sum of any two neighboring numbers is perfect square

2024 Kyiv City MO Round 1, Problem 2
Tags: arranging , parity , square , combinatorics
Is it possible to write the numbers from $1$ to $100$ in the cells of a of a $10 \times 10$ square so that: 1. Each cell contains exactly one number; 2. Each number is written exactly once; 3. For any two cells that are symmetrical with respect to any of the perpendicular bisectors of sides of the original $10 \times 10$ square, the numbers in them must have the same parity. The figure below shows examples of such pairs of cells, in which the numbers must have the same parity. [img]https://i.ibb.co/b3P8t36/Kyiv-MO-2024-7-2.png[/img] [i]Proposed by Mykhailo Shtandenko[/i]

2017 Bosnia And Herzegovina - Regional Olympiad, 4
Tags: chess , arranging , knight , combinatorics
How many knights you can put on chess table $5 \times 5$ such that every one of them attacks exactly two other knights ?