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Here is that sequence!
Looking at the special sequence once again.
8 5 4 9 1 7 6 10 3 2 0
If they are spelled as in sequence -
Eight Five Four Nine One Seven Six Ten Three Two Zero
Yes, you got it right. They are in an alphabetical order.
A hiker comes across an intersection where three roads cross. He looks
for the sign indicating the direction to his destination city. He finds
that the pole carrying three city names and arrows pointing to them has
fallen. He picks it up, considers it, and pops it back into place,
pointing out the correct direction for his destination. How did he do
it?
This is how he did it!
What was the dilemma?
Since he knew very well from which city he came; he just oriented that arrow in right direction. And obviously hence rest of all arrows are pointed in the right directions as well. This is how he found his right way!
A look at the question first!
Let's first recall the formula for the calculation of area of a triangle.
Area of triangle = 1/2 x Base x Height
Let's assume the side of the square is 1.
Now the triangle with the pink shade & triangle opposite to it are similar triangles. Similar triangles are triangle whose sides are in proportion with each other.
Since here base of pink triangle is double of un shaded opposite triangle, the height of pink triangle must be double of that smaller triangle.
But together, heights of both triangles must be equal to side of the square i.e. 1.
And hence, height of smaller triangle must be 1/3 & that of pink 2/3. (h + 2h = 3 ; h = 1/3).
So,
Area of Pink Triangle = 1/2 x Base x Height = 1/2 x 1 x 2/3 = 1/3.
So the area of pink shaded part is 1/3rd of total area occupied by square.