I have been thinking about this part of the egg dropping puzzle now for a couple of days, but haven't been able to come up with a reason.
I don't understand why,if the egg doesn't break when dropped some floor n, the next time, rather than jumping up another n floors, instead we step up just (n-1) floors and then (n-2), (n-3) and so on.
One of the sites I was referring to says, it's because we have one less drop available if we have to switch to one-by-one floors, so the next floor we should try is floor n + (n-1). Similarly, if this drop does not break, we next need to jump up to floor n + (n-1) + (n-2), then floor n + (n-1) + (n-2) + (n-3) … We keep reducing the step by one each time we jump up, until that step-up is just one floor, and get the following equation for a 100 floor building
n + (n-1) + (n-2) + (n-3) + (n-4) + … + 1 >= 100
Just to reiterate, my question is, why in the subsequent iteration, the number of floors is n-1.
Web link I was referring to is this