MathDB
unit squares

Source: Ireland 1993

June 29, 2009
geometryrectangle3D geometrygeometry proposed

Problem Statement

(a) (a) The rectangle PQRS PQRS with PQ\equal{}l and QR\equal{}m (l,m∈N) (l,m \in \mathbb{N}) is divided into lm lm unit squares. Prove that the diagonal PR PR intersects exactly l\plus{}m\minus{}d of these squares, where d\equal{}(l,m). (b) (b) A box with edge lengths l,m,n∈N l,m,n \in \mathbb{N} is divided into lmn lmn unit cubes. How many of the cubes does a main diagonal of the box intersect?
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