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In Is the DMG 3/4 cover diagram incorrect? the question asker points out the diagram shown in the DMG implies 3/4th cover, but it's possible to get a better angle on the defender meaning they only have 1/2 cover.

To determine whether a target has cover against an attack or other effect on a grid, choose a corner of the attacker's space... trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle (including another creature), the target has half cover...

Diagram showing various approaches to getting cover, from the DMG pages 250 and 251

Is it mathematically possible to construct a scenario where only 3/4th cover is possible? Intuitively I can't think of a place to put the attacker in the diagram where one corner isn't able to get 1/2 cover by picking a better square, whilst still having some attack on the defender.

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Yes.

This does it:

enter image description here

Choosing any other corner gives full cover.

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  • \$\begingroup\$ That does it. Although I didn't state that the defender should stay put, I guess this works for the question as is. \$\endgroup\$ Jul 16 '20 at 11:14
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The original question you link to gives an example

If the attacker was moved one square to the north it would be 3/4 cover. Or do you think they meant "choose the closest corner"?

The diagram would then look like this:

enter image description here

From the optimal corner, only one line can see the corner of the enemy's space.

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    \$\begingroup\$ Interestingly this also provides another 3/4 cover avenue, from the upper left corner of the attacker \$\endgroup\$
    – Sdjz
    Jul 16 '20 at 14:16
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    \$\begingroup\$ @Sdjz If they have two ¾ cover, is that ½ cover, cover-and-a-half, or 9/16 cover? xD \$\endgroup\$ Jul 16 '20 at 20:41
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    \$\begingroup\$ @Chronocidal clearly it's \$(\frac 3 4 )^{0.5} = \sqrt {\frac 3 4}\$ \$\endgroup\$
    – Trish
    Jul 16 '20 at 22:21

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