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Bundeswettbewerb Mathematik 1976 Problem 2.2

Source: Bundeswettbewerb Mathematik 1976 Round 2

September 22, 2022

geometrygeometric transformationsquareequal areasTranslation

Problem Statement

Two congruent squares

Q

and

Q'

are given in the plane. Show that they can be divided into parts

T_1, T_2, \ldots , T_n

and

T'_1 , T'_2 , \ldots , T'_n

, respectively, such that

T'_i

is the image of

T_i

under a translation for

i=1,2, \ldots, n.