Q1. How is it the longest clue?
Ans. The clue has two million words in it. Therefore, it is the world's longest clue. It breaks all previous records for the world's longest crossword clue.
Q2. You can count 'a million times' literally and what is the purpose of repetition?
Ans. The question is ambiguous. In case people have any questions about this clue, the clue reads as follows:
1 Ac. No idea, no idea, no idea, no idea, no idea, ... , no idea (3, 1, 4)
The phrase "no idea" is repeated a million times. The purpose of the choice of words in a clue can be anything. I can think of at least two different reasons for repetition. Can you?
Q3. Is there a limit to the number of times the phrase "no idea" can be repeated?
Ans. No. In the way I have formulated the clue, there is no limit. That is why I said that the clue can be made as long as you want. Its cardinality in the following form is aleph-naught:
1 Ac. No idea, no idea, ..., <infinite times> (3,1,4)
Q4. Is this the longest crossword clue possible?
Ans. Yes. A crossword clue must consist of a sentence. A sentence must have the following grammar:
S => W S
S => W .
Therefore, a sentence cannot have cardinality greater than aleph-naught. This clue has cardinality aleph-naught. Therefore, this is the longest crossword clue possible.
By the way, this constitutes a mathematical proof that this is the world's longest crossword clue.
Update (7:35 pm): Another question just came in.
Q5. Just 'no idea' means "Not a clue". What is the purpose of repetition?
Ans. This clue needs to be "read properly". I will supply here the reading of the clue. Note that like poetry, it is assumed that a cryptic crossword clue must be "interpreted" or "read properly". I will supply the reading below.
The clue is in two parts.
The first part is the phrase "No idea". This clues the final answer "Not a clue". The second part is the rest of the clue "no idea, no idea, ..., no idea". This part is -not- a clue. It is just a long sentence. At least, this is the case in our first reading (call this Reading R1) of this clue. This yields the answer "Not a clue". Thus, the phrase "Not a clue" is clued in two different ways. This satisfies the requirements for a cryptic crossword clue.
There is another neat thing about the clue. The pragmatics of the English language are such that "Not a clue" is a more emphatic phrase than the phrase "No idea". So, as a whole, the repetitions make it sound like somebody is emphasizing the phrase "No idea". This leads us also to the answer "Not a clue".
Q6. What if I don't agree with your interpretation?
Ans. Just like poets are given poetic license, so are setters of cryptic crossword puzzles given license. Even if you don't agree with an interpretation, you must try and see how that reading may be reasonable.
Q7. You said you also set the world's largest crossword puzzle. Can you link to the world's largest crossword puzzle?
Ans. Yes. Since this clue itself is infinitely long, there is no point in going in the other dimension. A two dimension crossword puzzle can never be of cardinality greater than aleph-naught. Therefore, as a mathematician, I stop here. This is the world's largest crossword puzzle as well.
There is a certain beauty in keeping things compact. So, in the interest of compactness, I present to you below the world's largest crossword puzzle in compact notation.
1 Ac. No idea, no idea, no idea, <repeated a million times> (3, 1, 4)
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Ans. This question is left as an exercise for the reader.