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3 Answers
- PuzzlingLv 75 years ago
The design is essentially a square, but with the 4 corners removed.
Design 1 is a 3 x 3 square with 4 corners removed.
Design 2 is a 4 x 4 square with 4 corners removed.
Design 3 is a 5 x 5 square with 4 corners removed.
Design 4 is a 6 x 6 square with 4 corners removed.
In general, for design N it would be an (N + 2) x (N + 2) square with 4 corners removed.
f(n) = (n + 2)² - 4
f(n) = n² + 4n + 4 - 4
f(n) = n² + 4n
Double-check:
f(1) = 1 + 4 = 5
f(2) = 4 + 8 = 12
f(3) = 9 + 12 = 21
etc.
- ?Lv 75 years ago
Well,
the function is
f(n) = n^2 + 4n
f(1) = 1^2 + 4*1 = 5
f(2) = 2^2 + 4*2 = 12
etc.
hope it' ll help !!
- llafferLv 75 years ago
If you need to count the number of diamonds based on the size of the row, note that only the corners are removed.
So square the size of the row, then subtract from 4:
f(x) = x² - 4
