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.
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” !!!
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.
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
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.
nobody :: feb 12 2007 :: 5:10 pm
Thank you, Nobody. I had seen that a while ago and was confused how this could have been missed.
flibbitygibbit :: feb 19 2007 :: 8:24 am
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.
Al :: apr 24 2007 :: 6:43 pm
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” !!!
Mahe :: may 24 2007 :: 3:25 am
it `s too difficult
hassan :: jun 24 2007 :: 9:22 am
These aren’t triangles so end of discussion.
Nuno José :: jan 01 2008 :: 6:19 pm
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!
C M Hoover :: oct 19 2008 :: 4:44 pm
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.
Ran Flam :: dec 31 2008 :: 10:16 am
not a feasible re-arrangement
ralph :: jan 09 2009 :: 3:58 pm
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.
ralph :: jan 09 2009 :: 4:55 pm
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
ralph :: jan 10 2009 :: 7:16 pm