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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.
Or a look at the question itself?
Let's look at the puzzle once again.
From first equation, it is clear that figure = 15. But the figure itself made up of square (4 sides) + polygon (5 sides) + hexagon (6 sides) = 15.
From second equation, we have bunch of 4 bananas = 4 i.e. 1 banana = 1.
And from third equation, we have 3 hours in clock = 3 i.e. 1 hours = 1.
Hence, in fourth equation, value of clock = 2, 3 bananas = 3, figure = sides of hexagon + sides of pentagons = 6 + 5 = 11.
2 + 3 + 3 x 11 = 38
Hence, answer is 38.
Bruce is an inmate at a large prison, and like most of the other prisoners, he smokes cigarettes. During his time in the prison, Bruce finds that if he has 3 cigarette butts, he can cram them together and turn them into 1 full cigarette. Whenever he smokes a cigarette, it turns into a cigarette butt.
One day, Bruce is in his cell talking to one of his cellmates, Steve.
“I really want to smoke 5 cigarettes today, but all I have are these 10 cigarette butts,” Bruce tells Steve. “I’m not sure that will be enough.”
“Why don’t you borrow some of Tom’s cigarette butts?” asks Steve, pointing over to a small pile of cigarette butts on the bed of their third cellmate, Tom, who is out for the day on a community service project.
“I can’t,” Bruce says. “Tom always counts exactly how many cigarette butts are in his pile, and he’d probably kill me if he noticed that I had taken any.”
However, after thinking for a while, Bruce figures out a way that he can smoke 5 cigarettes without angering Tom. What is his plan?
That's his master plan!
