How many squares of all sizes arise using an ๐‘›-by-๐‘› checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length ๐‘› ?

hifadhinitz 2022-09-04 Answered
How many squares of all sizes arise using an ๐‘›-by-๐‘› checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length ๐‘› ?
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Answers (1)

Sarahi Gallegos
Answered 2022-09-05 Author has 4 answers
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.
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