In 1 and 2, the thinking is not the type being referred to in the quote.

The quote is without a provenance that I can discover. If authentic, I presume that Patton was referring to military planning. I don't see a line separating that type of thinking from cases (1)-(4) and some of (5). Ideas must be found or created to achieve results that are not totally ordered. Thinking better is helpful but thinking alike is not.

In 3, assuming only one of theirs get chosen, then there are 19 failures, hence 19 non-thinkers or non-sufficient thinking.

Only if you "thinking better" to retroactively mean "won". But that is not what the word "thinking" means.

In 4, they're not all trying to answer the same question "what's the best way to make money", but the question "what's a good way to make money".

I doubt any of those entrepreneurs are indifferent between a given level of success and 10 times that level.

In 5, yes, every test-taker should give the correct answer to every question. Obvious for multiple choice tests, and even other tests usually only have one really correct answer, even if there may be more than one way to phrase it.

Perhaps you are thinking only of a limited type of exam. There is only one correct answer to "what is 23 times 87?"[1] Not all exams are like that.

Philosophy:

Do we need a notion of innateness in order to explain how humans come to know about objects, causes, words, numbers, colours, actions or minds? (Your answer may focus on a single domain of knowledge.)

Ancient history (from here:

"The mother of the King of Upper and Lower Egypt, follower of Horus, she who is in charge of the affairs of the Harem, whose every word is done for her, daughter of the god (begotten) of his body, Hetepheres." -- Inscription from the tomb of Hetepheres

With reference to the quotation, discuss the power and influence of queens in this period [of ancient Egypt].

The link also provides the marking criteria for the question. The ideal result can only be described as "twenty students giving the same answer" if, as in case (3), "the same answer" is redefined to mean "anything that gets top marks", in which case it becomes tautological.

In 6, first of all, your example is isomorphic to its complement; where 20 people decide not to lynch an innocent man. If you defend the original quote, then some of them must not be thinking. And the actual answer is that my quoted version is one-sided; agreement doesn't imply idealism, idealism implies agreement.

I reject both of those. Agreement doesn't imply ideal, of course (case 6 was just a test to see if people were thinking). But neither does ideal imply agreement, except by definitional shenanigans. And your version of Patton's quote doesn't include the hypothesis of ideality anyway. Neither does Patton's. We are, or should be, talking about the real world.

I could add a disclaimer; everyone should be thinking alike in cases referred to by the first quote. I don't have a good way to narrow down exactly what that is off-hand right now, it's kind of intuitional. Do you have an example where my claim conflicts directly with what the first quote would say, and you think it's obvious in that scenario that they are right and not me?

What are those cases? Military planning, I am assuming, on the basis of who Patton was. Twenty generals gather to decide how to address the present juncture of a war. All will have ideas; these ideas will not all be the same. They will bring different backgrounds of knowledge and experience to the matter. In that situation, if they all all agree at once on what to do, I believe Patton's version applies.

(1) Ubj znal crbcyr'f svefg gubhtug ba ernqvat gung jnf "nun, urknqrpvzny!" Whfg...qba'g.