Centy wrote:

Wonder what the IMO markers would make of a perfect solution written in L33tsp33k?

I think it would basicly depend on how readable it is. If it is still mathematically correct and understandable, it shouldn't be much of a problem. Not long ago, I ended a solution to a problem with a quote from Munchkin, what somewhat irritated the correcter, but it still was 7/7. At the most recent TST, I have defined an operation on graphs called "haxxoring" (really, I had no time and no better word came into my mind

) and enclosed a part of my solution which I found unnecessary in a <spam> </spam> tag. Participants should have the right to have some fun on exams. Of course, it starts suxx0ring when all the solution is written in 1337, what makes it hard to read normal words and distinguish between letters and numb3rz.

Centy wrote:

What is scarier is that beneath all the L33tsp33k, there's some really clever maths going on.

Well, may be, but this clever maths is over 100 years old

. Actually, it's an application of Miquel points. The basic fact is that four lines in the plane enclose four triangles, and that the circumcircles of these triangles have a common point; this point is called the Miquel point of the four lines. Now, the whole problem comes down to proving that the Miquel point of the lines AD, BC, AB, EF coincides with the Miquel point of the lines AD, BC, CD, EF; in other words, we have to prove that the circumcircles of triangles $X_{1337}AD$ , $X_{1337}BC$ and $X_{1337}EF$ have a common point. This is not only a simpler problem (we can forget about S and T now, the point $X_{1337}$ is much easier to handle), but also known: it is a restatement of http://www.mathlinks.ro/Forum/viewtopic.php?t=68157 .

Darij