Question 5
Let $n$ be a positive integer. Call two integer $n$-tuples $(a_1,\ldots,a_n)$ and $(b_1,\ldots,b_n)$ an exquisite pair if
$$|a_1b_1+\cdots+a_nb_n|\le1.$$
Determine the maximum number of distinct integer $n$-tuples such that every two distinct members form an exquisite pair.
Proposed by Pakawut Jiradilok and Warut Suksompong, Thailand.
$$|a_1b_1+\cdots+a_nb_n|\le1.$$
Determine the maximum number of distinct integer $n$-tuples such that every two distinct members form an exquisite pair.
Proposed by Pakawut Jiradilok and Warut Suksompong, Thailand.