How the answer is foundi
Closes in the planClick a floor to open it
Keep the least floor space open.
Ties go to the plan that moves fewer people.i
For each number of floors to close, it lists every combination, cheapest floor space first. That is at most 252 sets per count.
The first sets that seat everyone under the rules set the least floor space for that count. The solver proves the other sets impossible; it does not guess.
Among those sets, integer optimisation (HiGHS) finds the placement that moves the fewest people. It proves the result optimal and reruns live inside this file.