An n by 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∈N such that any s squares in an n−code (n≥4) form a key.
b.) Find the smallest t∈N such that any t squares along the diagonals of an n-code (n≥4) form a key. functionratioarithmetic sequencealgebrasystem of equationscombinatorics unsolvedcombinatorics