MathDB

An interstellar hotel has

100

rooms with capacities

101,102,\ldots, 200

people. These rooms are occupied by

n

people in total. Now a VIP guest is about to arrive and the owner wants to provide him with a personal room. On that purpose, the owner wants to choose two rooms

A

and

B

and move all guests from

A

B

without exceeding its capacity. Determine the largest

n

for which the owner can be sure that he can achieve his goal no matter what the initial distribution of the guests is.

Problem Statement