# How many squares of all sizes arise using an 𝑛-by-𝑛 checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length 𝑛 ?

How many squares of all sizes arise using an 𝑛-by-𝑛 checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length 𝑛 ?
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Sarahi Gallegos
It is very simple to see how many 1-squares fit. What about a 2-square (natural notation)? Well, let's only place the top-left square. How many places can we put the top-left square of a 2 by 2 on the board and have it fit? And so on? This leads to your intuition being correct.