Unit cubes are made into beads by drilling a hole through them along a diagonal. The beads are put on a string in such a way that they can move freely in space under the restriction that the vertices of two neighboring cubes are touching. Let A be the beginning vertex and B be the end vertex. Let there be p×q×r cubes on the string (p,q,r≥1).
(a) Determine for which values of p,q, and r it is possible to build a block with dimensions p,q, and r. Give reasons for your answers.
(b) The same question as (a) with the extra condition that A \equal{} B. geometry3D geometryanalytic geometryEulercombinatoricsIMO Shortlist