1)As 100/4=25,25=3m+1,the second win,my original proof is not good,but answer is right.This question is same as that there're 25 letters one can circles 1 letter or 2 connected letters,who circles the last is lost.
2)KMM is right,as 3^11>100000>3^10,11 is enought. I have a trick anwser,9 is enough only one day.
We can identify 9!+1=362880+1,code bottles,using permutation.code peoples,1,2,3,4,5,6,7,8,9.if bottle code is 736592148,letNO.1 takes 7g,No.2 take 3,...No.9 takes 8g. If it is poison,people die should be as this order 5,9,1,3,4,8,2,7.As 1 to 1,we can identify 9!+1.The formula is M=D*P!+1.D is number of days.P are the number of people.If 2 days M=725761.