Consider n 2 unit squares in the xy-plane centred at point (i, j) with integer coordinates, 1 ≤ i ≤ n, 1 ≤ j ≤ n. It is required to colour each unit square in such a way that whenever 1 ≤ i < j ≤ n and 1 ≤ k < l ≤ n, the three squares with centres at (i, k),(j, k),(j, l) have distinct colours. What is the least possible number of colours needed?

Motivated and talented Mathematics Faculty driven to inspire students to pursue their academic and personal excellence. Consistently striving to challenge and engaging learning environment in which students become life-long scholars and learners. Having an experience of more than 6 years in the education industry, having taught more than 5000 students, I decided to help students online. View all posts by M CUBE: Math-e-Matics by Maheshwari