n is a variable. It will indicate the worst case scenario and also the starting floor.
This is a sequence. You want the sum of the series to be >= 100 (lets call this X in case the number of floors change).
To find n, solve ((n*(n+1))/2) = X. Take the ceiling of n.
for our case this is ceiling(n(n+1)) = 200.
and our worst case scenario is 14 drops.
Our starting floor is 14.

The process to conduct the test:
Start at the 14th floor. Drop the widget.
If it breaks, take the second widget to the first floor and work your way up to the 13th floor until the second widget breaks. (if the second widget does not break by the 13th floor, then you know 14 is the lowest floor from which you can throw the widget that will cause it to break)
If it does not break, move up 13 floors (from the 14th to the 27th floor).
Repeat this process, decrementing the amount of floors by you climb between each non-break.
Assuming the widget does not break, you would visit floors:
14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, 100.
If the first widget breaks at any of these floors, simply take the second widget to the floor which is one above the last floor you successfully dropped the first widget from without it breaking (that is if you broke it on floor 69, go back down to 61 and work your way up to 68.

This is easy to recalculate if the amount of floors involved change. However if the amount of widgets provided change, your series will change as well.