Still didn't nap, still went to sleep at 11 PM, still woke up way too early.

Today was A G N which was the combination we decided was most likely.

- there is one N because there weren't any yesterday and there has to be one of each subject in each IMO
- there is almost certainly one G because it's typical and a lot of smaller countries like geo
- unless there are two Ns in one day (unlikely), #4 can't be N because putting the only N there would make its "weight" too small, so people good at number theory wouldn't have any place to show it
- #4 almost certainly won't be G because then both Gs would be easy problems
- #4 is unlikely to be C because last year that was what it was
- hence #4 is most likely A.
- this leaves G and N for #5 and #6, but last year's #5 and #6 were N G in that order, hence the likeliest order is the reverse.

#4. Functional equation on integers. Not very hard, but quite detailed and with some moderately pathological solution classes. After a magical factorization and an equivalence transformation into an auxiliary function, 1:35 finish.

#5. Geometry. Bad news, I had no idea how to use . I played around with trig and showed the target statement equivalent to concurrence of the angle bisector of , , and . Then at 2:15 from start I realized that was simply one Ceva and facepalmed. After enough lack of progress, I moved on.

2:30 switch to #6, which I wasn't entirely certain was N; it seemed like it could involve more algebra with bounding expressions. I found trivial solutions and considered primes and stuff trying to disprove the existence of most solutions. Then I tried to construct solutions and realized there were way too many for the answer to be a finite number of values. Stupid, stupid, stupid.

Parity argument disproving cases and only hit me at 3:00, while trying to construct . I found how to induct from to , and spent an hour trying various ways to induct to a , first with a +3 jump, then with +4, then after a long time +8, but then the deadline panic was starting to set in. I could do some cases like to , but none of my cases fit together to do anything. OA has faint memories of the official solution inducting with a gap of +12. The sense of progress failed me.

I went back and jotted down header information, then a small number of probably useless observations for the geometry, including ten minutes used to recall which Ceva it was I had discovered.

Ding-ding-ding.

Okay so score prediction

ridiculously pessimistic: 673/600
pessimistic/expected: 773/701 (I really don't think there will be logic holes; already got info on marking scheme partials from leader and OAs)
optimistic: 774/702
ridiculously optimistic: 775/714

With me not getting #5, I think a gold medal is unlikely. That's all for now.