MathDB

4

Part of 2013 Bosnia And Herzegovina - Regional Olympiad

Problems(2)

Regional Olympiad - FBH 2013 Grade 9 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013

9/24/2018
a)a) Is it possible, on modified chessboard 20×3020 \times 30, to draw a line which cuts exactly 5050 cells where chessboard cells are squares 1×11 \times 1 b)b) What is the maximum number of cells which line can cut on chessboard m×nm \times n, m,n∈Nm,n \in \mathbb{N}
combinatoricsChessboard
Regional Olympiad - FBH 2013 Grade 11 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013

9/24/2018
If A={1,2,...,4s−1,4s}A=\{1,2,...,4s-1,4s\} and S⊆AS \subseteq A such that ∣S∣=2s+2\mid S \mid =2s+2, prove that in SS we can find three distinct numbers xx, yy and zz such that x+y=2zx+y=2z
combinatoricsset