MathDB
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 11 is to be divided by rectangular panels of common width 11 and denominations long a1a_1, a2a_2, a3a_3, .... . . be paved without gaps (a11a_1 \ne 1). From the second panel on, each panel is similar but not congruent to the already paved part of the strip. When the first nn slabs are laid, the length of the paved part of the strip is snsn. Given a1a_1, is there a number that is not surpassed by any sns_n? The accuracy answer has to be proven.