3
Part of 1997 May Olympiad
Problems(2)
10000 equal equilaterals
Source: III May Olympiad (Olimpiada de Mayo) 1997 L2 P3
9/17/2022
There are equal tiles in the shape of an equilateral triangle. With these little triangles, regular hexagons are formed, without overlaps or gaps. If the regular hexagon that wastes the fewest triangles is formed, how many triangles are left over?
combinatoricscombinatorial geometry
10 checkers on a 8x8 board
Source: III May Olympiad (Olimpiada de Mayo) 1997 L1 P3
9/17/2022
On an board, checkers have been placed, each occupying a square. On each square without a token, a number between and is written, which is equal to the number of tokens placed on its neighboring squares. Neighboring cells are those that have a side or a vertex in common. Give a distribution of the tiles that makes the sum of the numbers written on the board the greatest possible.
combinatorics