Programming Brain Teaser #2: Self-reference

The correct answer is RQRQ.

Also, it is the only self-referencing statement in our programming language.

Why?
Any possible statement that names something must use one of the following patterns:

• Qx
• RQx
• RRQx
• RRRQx
• R…RQx

First of all, self-referencing statement cannot be of form Qx, because it names x, and these two statements differ in length (by 1, the length of Q). I.e.   | Qx |   !=   | x |.

Let’s take RQx then.
If | x | = 1 , the result will be of length 2, but | RQx | = 3 . And since 3 != 2, this won’t work.
If | x | = 2 , the result will be of length 4, and | RQx | will be also of length 4. So then RQx = xx. This works for x = RQ, and we get our self-referencing statement RQRQ.
If | x | > 2 , the result will always be longer than | RQx |.

Now, let’s take RRQx in turn.
If | x | = 1 , the result will be of length 4, and | RRQx | = 4 . Here we get RRQx = xxxx, and for this to work, x would have to be R and Q at the same time. Fails.
If | x | > 1, the result will always be longer than | RRQx |.

For R…RQx and statements with three or more R’s at the beginning, the resulting statement is always longer than the length of “program” creating that particular statement.

All in all, there is just one self-referencing statement, and that statement is RQRQ.

Side note: and yes, the idea behind quine program in your favorite programing language is the same: take part of your program, quote it (make it a string out of it), and print it twice.