Sentence Correction

Cartographers have long struggled with the problem of having the spherical Earth to draw on a flat sheet of paper.

(A) having the spherical Earth to draw on a flat sheet of paper
(B) having a flat sheet of paper on which to draw the spherical Earth
(C) how can one draw the spherical Earth on a flat sheet of paper
(D) how they could use a flat sheet of paper to draw the spherical Earth
(E) how to draw the spherical Earth on a flat sheet of paper

OA E

couldn't give a detailed explanation

Choose E
eliminated A and B because how ... seemed right

C and D seems wordy
also felt D gave more importance to paper than drawing itself
E simple and concise

A. B C anyway out..
in D - the menaing is coming like ..rather using a pen or pencil they tried to draw using the paper...

E is obvious.

In option E, shouldn't 'how to draw...' require a subject? Pls clarify

the sentence should be like this..
Cartographers have long struggled with the problem of drawing the spherical Earth on a flat sheet of paper.

but as per options E is correct

Can anybody please explain me why "problem of how" is better than "problem of having"

I would like to know the ONE used in choice C points to Cartographers or not. And is C incorrect because one is singular and Cartographers is plural.. ?? Please Help...