MathDB

n

n

grid, where every square contains a number, is called an

n

-code if the numbers in every row and column form an arithmetic progression. If it is sufficient to know the numbers in certain squares of an

n

-code to obtain the numbers in the entire grid, call these squares a key. a.) Find the smallest

s \in \mathbb{N}

such that any

s

squares in an

n-

code

(n \geq 4)

form a key. b.) Find the smallest

t \in \mathbb{N}

such that any

t

squares along the diagonals of an

n

-code

(n \geq 4)

form a key.

Problem Statement