@gemmi I am not sure about the right answer but I can tell you one of the fastest way to do it. It works like a search tree. Lets consider t be the time from when the mouse starts to show abnormal effects. First lets divide the bottles into 10 groups 100 each. Then mix the water from all the bottle of each group and make one water solution for each group. Now we make each mouse drink water from one of the solution and we note this down. After time t the mouse will start to show the effects of poison and we can identify which group the poisoned water is in. We discard the poisoned mouse and continue dividing again. Let me simulate the whole process. t=0 no of mice=10 bottles/group=100 t=1 no of mice=9 bottles/group=11 for 8 groups and 12 for a group t=2 no of mice=8 bottles/group= if group containing 11 bottles had poison:1 each for 5 groups and 2 each for 3 groups if group containing 12 bottles had poison:1 each for 4 groups and 2 each for 4 groups By now the chance of finding poisoned bottle is more than 50 % but there are groups with 2 bottles. t=3 no of mice=7 bottles/group=1 So the mininimum time require will be equal to 3t and maximum time will be equal to 4t This is just a method, the correct answer might suggest better method. for this method to work value of t should be 2.5 hrs.