Drop your first egg from the following floors until (or if) it breaks:

6th, 12, 18, 24, 30, 35

Worst case comes if the egg breaks on either the 30th or 35th floor.

If it breaks on the 30th floor, then take the second egg and start at 26 and go through 28, for a total of 8. You can skip 25, since you know 24 worked. No need to go past 28 because you know 30 didn't work.

If it breaks on the 35th floor, then take the second egg and start at 32 and go to 33, for a total of 8.

All other breaks result in less than 8.

Good puzzle. Thanks.

This does not work. Looking at your 35th floor example, you test the 35th floor on your 6th attempt. If the egg breaks there, then it must be either 31,32,33 or 34.

If you use your 2nd egg to start at 32, you're not attempting to break the egg at 31. Its possible that if you were to try it at 31, it would still break and the 30th floor would be the highest.