Question

Cubic Coprimes
Cubic Coprimes:Two integers are coprimes if their only common divisor is 1.For example,10 and 21 are coprime but 15 and 21 are not.Liam labels the vertices of a cube with eight different positive integers so that the labels on each pair of adjacent vertices are coprime.This is called a 'Liam labelling'.To make the edges of the cube easier to see,Liam uses this two-dimensional projection of the cube.
a) Find a Liam labelling using the integers 1 to 8.
b) Find a Liam labelling using integers in the range 2 to 10.
c) Explain why there is no Liam labelling using the integers 2 to 9.
d) Find a Liam labelling in which only composite numbers are used,and the largest label is as small as possible.Justify your answer.

Answer 1

This is the Australain Maths Competition questions. I advise for you to go and find the answers for yourself in the future. I will give you one answer
a) is the image attached