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Part of 2023 Novosibirsk Oral Olympiad in Geometry

Problems(2)

cut a 6x6 square into tiles 1x2 (2023 Novosibirsk Oral Geo Oly 7.1)

Source:

Let's call a corner the figure that is obtained by removing one cell from a

2 \times 2

square. Cut the

6 \times 6

square into corners so that no two of them form a

2 \times 3

3 \times 2

rectangle together.

geometrytilescombinatorial geometry

CD, BE divide ABC in 4 parts of same area ? (2023 Novosibirsk Oral Geo Oly 9.1)

Source:

In the triangle

ABC

AB

AC

D

and E are chosen, respectively. Can the segments

CD

BE

ABC

into four parts of the same area? https://cdn.artofproblemsolving.com/attachments/1/c/3bbadab162b22530f1b254e744ecd068dea65e.png