admit of?

I make the following attempts :

You never want to admit that your answer is a big joke.

You never want to admit of your answer is a big joke.

Hope it may help.

Your answer of which is a big joke (that) you never want to admit.

That your answer is a big joke is the object of admit, not just a big joke. Which should not be used at all.

Your answer is a big joke, a fact you never want to admit.

I also buy ed_young's answer.

2013-01-21 01:08:10 補充：
Answer 001's second sentence is wrong.

Jenkin wrote the sentence as an example of "of which" and not as a re-write of the original sentence. Unfortunately, the relative pronoun is not used correctly.

admit of = to grant opportunity or permission eg The contract admits of no other interpretation.
admit of something = to show that something is possible

2013-01-18 20:05:08 補充：
Both the above meanings of"admit of" do not seem to make sense in "Your answer is a big joke of which you never want to admit.".

2013-01-18 20:08:14 補充：
I think the original writer of the sentence mistook the sentence to mean "Your answer is a big joke which you never want to admit.".

2013-01-20 05:47:51 補充：
I agree. If 'your answer is a big joke' is the object of 'admit', "Your answer is a big joke, a fact you never want to admit" is correct.

2013-01-20 05:54:13 補充：
"You never want to admit of your answer is a big joke." does not seem to make sense.
"which no one takes seriously" does not mean " which you never want to admit".

If focus on the expression "X which", the correct expression is "which" or "that".

"of which" means the following sentence is to explain the details or effect of the first sentence.

For example:
Your answer is a big joke of which no one takes it seriously.
- this means no one take your answer seriously becuase it is being a big joke.

There are other "x which" expression:

in which
by which
to which
has to relate to the context of the first sentence "item" to the sepcific relation to the second sentence.

Bluedy has the best answer:
"You never want to admit that your answer is a big joke."
"Your answer is a big joke, but you would never admit it" is also okay.
Ironically the author of the original sentence is a bit of a joker, by criticizing others' English with bad English.

---An Attempt To Answer only, whether correct or not in expressions.--------
"That" can be used instead of of which in this meaning; but it is not used immediately after a preposition"to".
------That was a joke that you never want to admit "to".
---------Where are the missing words "answer" and " big" ?
------Answer:-That answer was a big joke that you never want to admit to.
Another answer:-
-------Your answer, which you never want to admit,
--------(adv.cl.of condition);
-------is but a big joke.
--------(but is conjunction used to introduce a word that contrasts with what was said before; and with the same meaning.)