We stumped you on this one. No student found the way of determining the shattering floor within five trials.
The Math Department proposes this solution:
Drop your first marble from Five. If it shatters, then proceed with your second marble from floor one and work your way up. (This implies that you will need no more than 5 trials.)
If it doesn't shatter, proceed to Nine. If it shatters from Nine, then proceed to Six and work your way up. (This implies that you will need no more than 5 trials.)
If it doesn't shatter, proceed to Twelve. If it shatters from Twelve, then proceed to Ten and work your way up. (This implies that you will need no more than 5 trials.)
If it doesn't shatter on Twelve, proceed to Thirteen. If it doesn't shatter, then there is no shattering height in the building. If it does shatter, it only took 4 trials to find out.