I think the answer is that the diagonal side of the larger and smaller triangles do not have the exact same degree of slope, and therefore depending on which arrangement the shapes are in, some of their area will actually be beyond a line drawn directly from the upper right corner to the lower left.

I've put together an exaggerated graphic at:

http://home.nycap.rr.com/swingshift/diagram.jpg

to illustrate what I'm saying, in case my language isn't clear.

I suspect the difference in area between the two arrangements is equal to one square of the grid, which is where the white square "comes from".

Really looking forward to Runaway Comic, by the way, although you're forcing me to break my moratorium on buying individual issues.

Here's a link to an archived copy of the missing explanation. It basically says what the above commenters have said. It's a trick. The angle of the triangles are not the same.

The Blue 5 by 2 triangle and the red 8 by 3 triangles are of different ratios. 5 by 2 is the same as 7.5 by 3; a half block smaller! My Trig is rusty but you can see that the blue triangle starts in the corner of block 1,1 and ends at the corner of block 5,2. On this same illustration without moving anything look at the line at block 8,3 where the red triangle WOULD meet IF it were in the lower position. It does not meet in the corner and I'm betting that this deviation is enough to account for the one square difference between the 5x3 and 8x2 rectangles form by the two formations of the triangles. That's my SWAG

## 8 comments:

play with it some more...you will see the triangles are really not equal...

ie. take the shapes from the top one and see how much they "stick out" when placed behind the triangle at the bottom....

it's a trick!

nope.

Seriously, I have re-arranged them on both grids, every which way but loose. That square really does vansih.

Mark--

I think the answer is that the diagonal side of the larger and smaller triangles do not have the exact same degree of slope, and therefore depending on which arrangement the shapes are in, some of their area will actually be beyond a line drawn directly from the upper right corner to the lower left.

I've put together an exaggerated graphic at:

http://home.nycap.rr.com/swingshift/diagram.jpg

to illustrate what I'm saying, in case my language isn't clear.

I suspect the difference in area between the two arrangements is equal to one square of the grid, which is where the white square "comes from".

Really looking forward to Runaway Comic, by the way, although you're forcing me to break my moratorium on buying individual issues.

It's simple: one of your dogs got it. The little beggars!

It all has to do with quantum.

slatts is right, those pieces go way over the edges of the squares. They scooted over just enough to give room for a square.

Either that or it's all the absinthe.

Here's a link to an archived copy of the missing explanation. It basically says what the above commenters have said. It's a trick. The angle of the triangles are not the same.

http://web.archive.org/web/20030207150930/garyboone.com/stories/2002/12/16/completeSolutionToTrianglePuzzle.html

-Chris

When re-arranged the shapes overlap the lines a bit, leaving just enough space for the "vanishing" square.

...but yeah, that's already been explained. :(

The Blue 5 by 2 triangle and the red 8 by 3 triangles are of different ratios. 5 by 2 is the same as 7.5 by 3; a half block smaller! My Trig is rusty but you can see that the blue triangle starts in the corner of block 1,1 and ends at the corner of block 5,2. On this same illustration without moving anything look at the line at block 8,3 where the red triangle WOULD meet IF it were in the lower position. It does not meet in the corner and I'm betting that this deviation is enough to account for the one square difference between the 5x3 and 8x2 rectangles form by the two formations of the triangles.

That's my SWAG

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