Binary prism
Source: Romanian District Olympiad 2006, Grade 10, Problem 3
March 11, 2006
geometry3D geometryprismcombinatorics proposedcombinatorics
Problem Statement
We say that a prism is binary if there exists a labelling of the vertices of the prism with integers from the set such that the product of the numbers assigned to the vertices of each face (base or lateral face) is equal to .
a) Prove that any binary prism has the number of total vertices divisible by 8;
b) Prove that any prism with 2000 vertices is binary.