How many rectangles can you make?
In an by grid, you can make different rectangles. The first few values of are given in the picture. (i.e. In a 1x1 grid, and ; In a 2x2 grid, and , etc)
If , what is the sum of the first and last digits of
Note: A square is also a rectangle.
The answer is 9.
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1 solution
There are many approaches to this problem.
Great explanation by RedpenBlackpen here: https://www.youtube.com/watch?v=Uq9OXC0Gzgw
Taking 2 ( 6 1 8 0 3 ) ( 6 1 8 0 4 ) we will get 1909836306
Squaring this, we will get a value that begins with 3 as the first two digits are within ( 1 8 , 2 0 ) (all of which results in 3 as the first digit 18000... = 3##... and 19999^2 = 3##... )
The last digit will be a 6 , as any number with 6 as it's last digit results in a final digit of 6 .
3 + 6 = 9