16 dots combinatorics 1
Use your imagination, make 16 dots in your mind ( or you can draw it). Arrange those dots into a big square (4 on each row, 4 on each column). The dots should be equally spaced. ( it should be like the photo above)
Now you have to connect 4 dots to make a square. How many squares can you make by using those 16 dots.
The answer is 20.
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1 solution
Moderator note:
How do you know that's all the cases?
Let's use casework.
Case 1:
There are 9 such squares.
Case 2:
There are 4 such squares.
Case 3:
There is 1 such square.
*Case 4:
There are 4 such squares.
Case 5:
There is 1 such square.
Case 6:
There is 1 such square.
Adding up 9 + 4 + 1 + 4 + 1 + 1 , we get 2 0 squares.