MathDB

Let

N>s

be positive integers. Electricity park has a number of buildings; exactly

N

of them are power plants, and another one of them is the headquarter. Some pairs of buildings have one-way power cables between them, satisfying: (i) The cables connected to a power plant will only send the power out of the plant. (ii) For each non-headquarter building, there is a unique sequence of cables that can transport the power from that building to the headquarter. A building is

s

-electrifed if, after removing any one cable from the park, the building can still receive power from at least

s

different power plants. Find the maximum possible number of

s

-electrifed buildings.
Note: There seems to be confusion about whether a power plant is

1

-electrified. For the sake of simplicity let's say that any power plant is not

s

-electrified for any

s\geq 1

.
Proposed by usjl

Problem Statement