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Part of 2011 Bundeswettbewerb Mathematik
Problems(2)
split a square into finitely many hexagons with inner angles all < 180^o
Source: Germany Federal - Bundeswettbewerb Mathematik 2011, round 2, p1
4/15/2020
Prove that you can't split a square into finitely many hexagons, whose inner angles are all less than .
squarehexagonTilingcombinatorial geometrytilesanglesgeometry
10 bowls with marbles in a circles
Source: Germany Federal - Bundeswettbewerb Mathematik 2011, round 1, p1
4/10/2020
Ten bowls are in a circle. They will go clockwise - starting somewhere filled with or marbles. You can have two choices in every move . Add a marble to neighboring shells or from two neighboring shells - if both of them are not empty - remove one marble each. Can you achieve that after finally many moves in each bowl exactly marbles lying?
combinatorics