Something Similar To Fibonacci Squares
1 2 + 1 2 + 1 2 + 3 2 + 4 2 + 7 2 + 1 1 2 = ?
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6 solutions
If you look at the squares from the top left, you will notice that we have
3 1X1 squares,
1 3X3 square,
1 4X4 square,
1 7X7 square,
1 11X11 square.
Hence, the area of the rectangle is 1 2 + 1 2 + 1 2 + 3 2 + 4 2 + 7 2 + 1 1 2 .
We can also calculate the area of the rectangle directly. Since it has a height of 11, and a width of 18, hence it has an area of 1 1 × 1 8 = 1 9 8 .
Thus, the area of the rectangle is 1 2 + 1 2 + 1 2 + 3 2 + 4 2 + 7 2 + 1 1 2 = 1 9 8 .
Unfortunately the final 11 squared was missing on my display, so I could not be certain what I was solving for.
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Can you send me a screenshot of what you saw? There should be a scrol bar to indicate that the Latex equation is incomplete.
You can email me: Calvin at Brilliant.org
And as an added easy way to multiply by 11. Take sum of first and second digit and place it in between the digits. 18x11 is 1(1+8)8 = 198.
Brilliant! But try 57. Does weird stuff. 5(5+7)7 is... [5(1],2)7...(brackets mine cuz they become the 6 in 627?). So is that a repeatable pattern if the two added numbers in parentheses equal double digits? Far left ones get added? (Like the two in my brackets?) 6(6+7)7 or [6(1]3)7or 737...huh... neato.
1 2 + 1 2 + 1 2 + 3 2 + 4 2 + 7 2 + 1 1 2 = 1 + 1 + 1 + 9 + 1 6 + 4 9 + 1 2 1 = 1 9 8
You can see that the rectangle formed by the square with a side length of 11. 198 is the only number that is a multiple of 11. You can do the same for the 18, which has a factor of 3. 198 is the only multiple of 3 ( 1 + 9 + 8 = 1 8 1 + 8 = 9 ) .
the hard way: count the squares
the easy way: 1 1 ∗ 1 8 do the math
Find out the area, which is 11 x 18
Find the area of the square given in the diagram.
Its length is 1 1 + 7 = 1 8 units and breadth is 7 + 4 = 1 1 units.
So, the answer is length × breadth = 1 8 × 1 1 = 1 9 8 sq.units.
Alternatively,
Addition = ( 1 + 1 + 1 + 9 + 1 6 + 4 9 + 1 2 1 = 1 9 8 )