tiling a strip of width 1 with rectangles
Source: 1991 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4
November 20, 2022
combinatoricscombinatorial geometrygeometryrectangle
Problem Statement
A strip of width is to be divided by rectangular panels of common width and denominations long , , , be paved without gaps (). From the second panel on, each panel is similar but not congruent to the already paved part of the strip. When the first slabs are laid, the length of the paved part of the strip is . Given , is there a number that is not surpassed by any ? The accuracy answer has to be proven.