MathDB

7

Part of 2022 Tuymaada Olympiad

Problems(2)

Tuymaada 2022

Source: Tuymaada 2022 Junior P-7

9/12/2022
MM is the midpoint of the side ABAB in an equilateral triangle △ABC.\triangle ABC. The point DD on the side BCBC is such that BD:DC=3:1.BD : DC = 3 : 1. On the line passing through CC and parallel to MDMD there is a point TT inside the triangle △ABC\triangle ABC such that ∠CTA=150.\angle CTA = 150. Find the ∠MTD.\angle MT D. (K. Ivanov )
geometryangle
Tuymaada 2022

Source: Tuymaada 2022 Senior P-7

9/12/2022
A 1×5n1 \times 5n rectangle is partitioned into tiles, each of the tile being either a separate 1×11 \times 1 square or a broken domino consisting of two such squares separated by four squares (not belonging to the domino). Prove that the number of such partitions is a perfect fifth power. (K. Kokhas)
combinatoricstielsdominorectangle