The pieces are the same size! They should take up the same space. The universe is playing tricks on me – and I hate that.
Popularity: 4% [?]
The pieces are the same size! They should take up the same space. The universe is playing tricks on me – and I hate that.
Popularity: 4% [?]
It’s a crappy drawing, meant to trick you. Note that, in the top drawing, the green triangle comes to a point on a grid intersection point. Follow the vertical line down, the red triangle doesn’t pass through that point: the shapes are NOT exactly the same. The extra area comes from the fact that the new triangle is slightly larger.
Thank you, Nobody. I had seen that a while ago and was confused how this could have been missed.
The crappiness of the drawing can’t help but when drawn perfectly to scale, in a CAD program for example, this “illusion” still holds true. With the base dimension of a simple 1 unit the larger triangle has a slope of (3 units)/(8 units)=.375 while the smaller has a slope of (2 units)/(5 units)=.400 which is just over 1° of difference. This produces a slight “sag” to the overall diagonal when the larger triangle is on the left and a slight bow when it is on the right. The area of this sliver of difference in fact equals the missing 1 square unit.
The hypotenuses of both the triangle have different slopes. So the overall big structure can’t be considered a triangle. If considered, the hypotenuse of the overall structure is bent inside in the first figure and bent outside in the second figure covering up larger area which came from the “hole” !!!
it `s too difficult
These aren’t triangles so end of discussion.
All of the above commenters are WRONG! If the drawing is accurately replicated in CAD, the areas of the blue (lower right) squares are 8 in both triangles. The yellow squares will have an area of 7 in one triangle and 6.992 in the other. one square has it’s upper left corner cut a bit. The red and green triangles are not proportional in size! In one the green is 4.808, while the red is 11.700, and in the other the green is 5.200 while the red is 12.300. Addition shows that the difference in the colored squares are exactly 1 apart; 31.5 to 32.5. Clever!
The puzzle clearly indicates that the “same shapes” have been moved around. You’re susggsting slighly different shapes (in size). I don’t think this is theright answer.
not a feasible re-arrangement
the base of both red triangle’s are both 8 blocks long from left to right. The triangular space above, in which it will be moved, is only 7 1/2 blocks from left to right.
Count the blocks to see that the relationship between both triangles and the space in which they are to be moved are diffreent.
count all the colored blocks as full blocks by including the ones that are mixed with white and you will find that both diagrams use 40 blocks that include the so called hole
the hole is not a hole, it belongs there
just calculate the angle for both triangles.the angle for red triangle is arc tan 3/8=20.55 degree. green triangle :arc tan (2/5)=21.8 degree..this proves that the slope for both triangles is not the same which make the space