I feel like I might just be misunderstanding what the question is asking but I think “how many people will know about the rumor on the 7th day” is a bit ambiguous since it can refer to the number of new people who are told on that day, which seems to be what the question is actually asking, or the number of total people who know about it at the end of the day, which is my interpretation of it. So my calculations were that there were 16038 new people told and 8019 people who already knew before, so that 24057 people know about the rumor on the 7th day.

Second, question 20 is also a bit weird. As it ignores the fact that V can be 0 as it is not present at the start of either TUV or UVT. Using this fact we can find an answer that is even smaller than 148. I think 130 is the actual solution to this question as

301-130=171 which is a palindrome.