I got 34 as the minimum.

First, you test floor 3.
-If it breaks, try floor 1.
-If it doesn't break at 1, try floor 2.

Second, you test floor 6.
-If it breaks, try floor 4.
-If it doesn't break at 4, try 5.

Using this by three-method, you will get up to 99 throwing it 33 times(100 divided by 3=33r1) then you have to do it just one more time for the 100th floor, so 33+1=34, and then you're done!!!!!