MathDB

4

Part of 2018 Serbia Team Selection Test

Problems(1)

Dividing a rectangle into trapeziums.

Source: 2018 Serbia TST P4

9/22/2019
An isosceles trapezium is called right if only one pair of its sides are parallel (i.e parallelograms are not right). A dissection of a rectangle into nn (can be different shapes) right isosceles trapeziums is called strict if the union of any i,(2≤i≤n)i,(2\leq i \leq n) trapeziums in the dissection do not form a right isosceles trapezium. Prove that for any n,n≥9n, n\geq 9 there is a strict dissection of a 2017×20182017 \times 2018 rectangle into nn right isosceles trapeziums.
Proposed by Bojan Basic
combinatoricstrapezoid