Got this one from a friend. We both can't stand that we can not find the explanation for it. But we're both not very good at mathematics. Any of you?
Louis (who lacks intelligence for this)
Louis (who lacks intelligence for this)
Puzzle!
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frontaloadotmy
Well-known member
That hole
Can best be described as the "obtuse" effect!
Beats me!!!!
Can best be described as the "obtuse" effect!
Beats me!!!!
since we are not dealing with a triangle here...
...it makes sense that the shapes don't line up. My trig. is too rusty to explain it mathematically, but a close look at the "overall" triangles will show that they are, in fact not triangles, but four sided objects.
(Well, one thing does occur to me...the area covered by a real triangle would be 1/2 of (5*13) or 32.5 blocks. But I come in too low or high on the areas on both...)
Anybody here who can do the real math? That was just my "kitchen chemist" button-for-a head solution...
...it makes sense that the shapes don't line up. My trig. is too rusty to explain it mathematically, but a close look at the "overall" triangles will show that they are, in fact not triangles, but four sided objects.
(Well, one thing does occur to me...the area covered by a real triangle would be 1/2 of (5*13) or 32.5 blocks. But I come in too low or high on the areas on both...)
Anybody here who can do the real math? That was just my "kitchen chemist" button-for-a head solution...
The trick is to count the squares, they are the unit of measurement.
The orange shape and the light green shape are similar, but the orange shape has its thick part two squares long and its thin part three squares long.
The light green shape has its thick section three squares long and its thin section two squares long.
If you stack them with the orange shape precisely on top of the light green one, they fit neatly together.
If you move the shapes over one square to the left and down one square, they now fit with a gap because the two thinner sections are different lengths.
So why do the four pieces combine to form two identical triangles, with a square missing from one triangle??
The answer is they don't. It is an illusion. The red triangle is 8 long and 3 high, giving a slope of 8 in 3 or 2.66666. The green triangle is 5 long and 2 high, giving a slope of 5 in 2 or 2.5. So the sloping side (hypotenuse) of both triangles looks like they form one line but they don't, the green triangle is steeper than the red one.
The extra space comes because the overall shape bulges inwards slightly on the first shape and outwards slightly on the second shape. The difference is equivalent to the square.
The overall "triangles" appear the same but they are not. In fact there is NO overall triangle, it is actually a 4 sided figure. The hypotenuse of the green triangle and the hypotenuse of the red triangle are NOT in line, they form two sides of the overall shape. The OVERALL surface area of the two shapes are exactly the same, even though one looks like a regular triangle and one looks like a triangle with a bit missing. Remember, the overall shapes are NOT triangles at all.
Chris.
Thanks Louis, what a great puzzle!!
I love these sort of brain teasers.
The orange shape and the light green shape are similar, but the orange shape has its thick part two squares long and its thin part three squares long.
The light green shape has its thick section three squares long and its thin section two squares long.
If you stack them with the orange shape precisely on top of the light green one, they fit neatly together.
If you move the shapes over one square to the left and down one square, they now fit with a gap because the two thinner sections are different lengths.
So why do the four pieces combine to form two identical triangles, with a square missing from one triangle??
The answer is they don't. It is an illusion. The red triangle is 8 long and 3 high, giving a slope of 8 in 3 or 2.66666. The green triangle is 5 long and 2 high, giving a slope of 5 in 2 or 2.5. So the sloping side (hypotenuse) of both triangles looks like they form one line but they don't, the green triangle is steeper than the red one.
The extra space comes because the overall shape bulges inwards slightly on the first shape and outwards slightly on the second shape. The difference is equivalent to the square.
The overall "triangles" appear the same but they are not. In fact there is NO overall triangle, it is actually a 4 sided figure. The hypotenuse of the green triangle and the hypotenuse of the red triangle are NOT in line, they form two sides of the overall shape. The OVERALL surface area of the two shapes are exactly the same, even though one looks like a regular triangle and one looks like a triangle with a bit missing. Remember, the overall shapes are NOT triangles at all.
Chris.
Thanks Louis, what a great puzzle!!
I love these sort of brain teasers.
Boy this one has heads scratching doesn't it. When I started typing, there were no responses. By the time I posted, two people had beaten me to it!!!
Chris.
Chris.
The square hippopotamus had sum fun equally on both square slides.
Me hates those puzzles.
Me hates those puzzles.
I purposely didn't read the responses until I had figured this one out...
If the internal area of both arrangements were equal, then there shoudl be no unfilled spaces.
But they are not equal. It's an optical illusion. One assumes that the red and blue triangles have the same slope, and that the area of each arrangement is equal, but this is in fact not the case. The clue I had to this is that the open spaces near the mid-point of the complete figure's "hyptenuse" were not equal between arrangements. Then I took a straight edge to the screen and noted that the upper triangle has a concave hyptenuse, whereas the lower triangel has a convex hypotenuse. This slight difference in area is enough to account for the unfilled square at the bottom of the second arrangement.
If the internal area of both arrangements were equal, then there shoudl be no unfilled spaces.
But they are not equal. It's an optical illusion. One assumes that the red and blue triangles have the same slope, and that the area of each arrangement is equal, but this is in fact not the case. The clue I had to this is that the open spaces near the mid-point of the complete figure's "hyptenuse" were not equal between arrangements. Then I took a straight edge to the screen and noted that the upper triangle has a concave hyptenuse, whereas the lower triangel has a convex hypotenuse. This slight difference in area is enough to account for the unfilled square at the bottom of the second arrangement.
jasonl
New member
On the top piece, the orange piece is on top and on the other one, the orange is on the bottom with its opening exposed.
(ducks and runs)
(ducks and runs)
Well this is similar to that perplexing situation you find yourself in when you buy something new in a box, like a cordless phone etc. Take all the styrofoam packaging out, decide you don't like it, then try and fit it all back in the box so you can return it, impossible.
As a regular Costco customer, I have become adept at figuring out how to repack various gadgets back into their styrofoam/cardboard coffins for return/full refunds. It's not too hard when the styrofoam is molded to match the outer contours of the product. The ones that are lost causes are the big furniture/cabinet pieces that are made of individual flimsy styro strips that are taped to cardboard or just left loose. These are nearly impossible to get back into place. But in most cases Costco doesn't care about the, and in most cases I don't return such large items.
Thank you Chris!!
