MathDB

A hundred tourists arrive to a hotel at night. They know that in the hotel there are single rooms numbered as

1, 2, \ldots , n

, and among them

k{}

(the tourists do not know which) are under repair, the other rooms are free. The tourists, one after another, check the rooms in any order (maybe different for different tourists), and the first room not under repair is taken by the tourist. The tourists don’t know whether a room is occupied until they check it. However it is forbidden to check an occupied room, and the tourists may coordinate their strategy beforehand to avoid this situation. For each

k{}

find the smallest

n{}

for which the tourists may select their rooms for sure.
Fyodor Ivlev

Problem Statement