Nair has puzzle pieces shaped like an equilateral triangle. She has pieces of two sizes: large and small.
https://cdn.artofproblemsolving.com/attachments/a/1/aedfbfb2cb17bf816aa7daeb0d35f46a79b6e9.jpg
Nair build triangular figures by following these rules:
∙ Figure 1 is made up of 4 small pieces, Figure 2 is made up of 2 large pieces and 8 small, Figure 3 by 6 large and 12 small, and so on.
∙ The central column must be made up exclusively of small parts.
∙ Outside the central column, only large pieces can be placed.
https://cdn.artofproblemsolving.com/attachments/5/7/e7f6340de0e04d5b5979e72edd3f453f2ac8a5.jpg
Following the pattern, how many pieces will Nair use to build Figure 20? algebracombinatorial geometrycombinatorics