NCERT Carpet - Rn and Hn - Exploring Some Geometric Themes

Question: For the Sierpinski Carpet, find formulas for the number of remaining squares Rn and the number of holes Hn at step n.

Answer: Rn = 8^n; H0 = 0 and Hn = (8^n - 1)/7 for n >= 1.

Full step-by-step NCERT solution with diagrams on Something by Zero.