Problems(3)
max no of pieces, same perimeter, chessboard (2020 Novosibirsk Oral Geo Oly 8.2)
Source:
5/20/2021
Vitya cut the chessboard along the borders of the cells into pieces of the same perimeter. It turned out that not all of the received parts are equal. What is the largest possible number of parts that Vitya could get?
geometryperimeterChessboardcombinatorics
3 /4 sides of any quadr., create triangle? (2020 Novosibirsk Oral Geo Oly 7.2)
Source:
4/27/2021
It is known that four of these sticks can be assembled into a quadrilateral. Is it always true that you can make a triangle out of three of them?
geometrytriangle inequality
cut diagonal of 2x2 in 6 equal parts, ruler (2020 Novosibirsk Oral Geo Oly 9.1)
Source:
5/24/2021
A square was cut out of a sheet of grid paper. Using only a ruler without divisions and without going beyond the square, divide the diagonal of the square into equal parts.
geometryRulerconstructionsquare