IBM Ponder This #154 · February 2011

We define flip(n) as writing the integer n in seven-segment font and flipping it (rotating it 180 degrees). For example, flip(168)=891. The flip operation is only defined for digits that have a numerical meaning when flipped. For example, the digit "4" becomes the letter "h", which is not a digit, so the flip operation is not defined for numbers like 4 or 141.
If flip(n) is well-defined, we call n a flippable number.
Find an integer n > 0 for which all of the following three conditions hold:
A. n is flippable and flip(n) = n.
B. n*n is flippable.
C. n is divisible by 2011.

For example,

(192555261) satisfies conditions A and C but not B, since n*n starts with the unflippable digit 3.

For extra credit, send us another integer that satisfies conditions A, B, and the new condition C': n divided by 2011 leaves a remainder of 100.
Correct solutions to the extra credit challenge will earn solvers a star next to their names.

Update: February 4th: Note that flipping "2" gets a "2", not "5".

Solution

Best opened after a real attempt

To be added.