Please ignore this question
I came across the brilliant 100 prisoners and a secret number and have a potential solution which I can't find any flaw with. Can you please let me know what I'm missing.
Solution: In a pre-planned way, prisoner 1-10 guess 10,20,30 .. 100. If they see a larger number on the envelope, they leave it face up else face down. Everytime a prisoner see a face down envelope, they guess 1 less than the previous prisoners guess. For example, if the 5th prisoner turns the envelope face down, 6th guesses 49, 7th guesses 48 and so on...
This strategy can ensure that 81 prisoners survive at the end which is higher than the proposed solution.