Question 17
(NET 3) 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 $p\times q\times r$ cubes on the string $(p,q,r\ge1)$.
(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 $A=B$.
(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 $A=B$.