Some pending matters.
Asked in Mouse-ying along to the music about Tom playing Liszt's Hungarian Rhapsody #2. In case you missed the discussion in the comments, that's Tom of the cartoon pair Tom and Jerry, and I'm referring to the 1946 Oscar-winning Cat Concerto. Tom plays the piano, to much trouble-making and usual fun from Jerry, but Jerry soaks in the applause at the end.
In Rana on the board, I had a picture and asked if anyone could recognize where it was taken. Again in case you missed the vital discussions in the comments, that was taken at IIT Kanpur, during the 1978 Cultural Festival. That's members of the audience on the stage during a skit that I was part of. As I mentioned in passing to one of the people who commented there, there are at least a couple of names discernible among all that's written on that board. It would be a delight to run into Himadri Rana or Shahana Das Gupta one day and say: hey, I have a picture in which your name is up on the board! (I expect them to give me strange looks).
100-statement question was for the logicians. For an answer, I can do no better than point you to the comments there, especially to Sailesh Ganesh's detailed explanation. I like this problem, and the exercise of thinking about it.