Question 4
The country of Squareland is shaped like a square and is divided into $64$ congruent square cities. We want to divide Squareland into states and assign to each state a capital city so that the following rules are satisfied:
a. Every city lies entirely within one state.
b. Given any two states, the numbers of cities in them differ by at most $1$.
c. Any city in a state shares at least one corner with the state's capital.
What is the smallest possible number of states?
a. Every city lies entirely within one state.
b. Given any two states, the numbers of cities in them differ by at most $1$.
c. Any city in a state shares at least one corner with the state's capital.
What is the smallest possible number of states?