MathDB

2

Part of 2022 Kosovo & Albania Mathematical Olympiad

Problems(2)

Coloring a grid

Source: KAMO 2022 Grades 7-8 P2

7/5/2022
Consider a 5×55\times 5 grid with 2525 cells. What is the least number of cells that should be colored, such that every 2×32\times 3 or 3×23\times 2 rectangle in the grid has at least two colored cells?
rectanglecombinatorics
Relation in a convex quadrilateral formed from an acute triangle

Source: KAMO 2022 Grade 9 P2

7/5/2022
Let ABCABC be an acute triangle. Let DD be a point on the line parallel to ACAC that passes through BB, such that ∠BDC=2∠BAC\angle BDC = 2\angle BAC as well as such that ABDCABDC is a convex quadrilateral. Show that BD+DC=ACBD + DC = AC.
geometryrectangle