# Impossible Puzzle

My idea below the fold.

The a small gap around the larger pieces. When these pieces are rearranged, that small gap is accumulated into one condensed area. Note the alignment of the center line with the smaller pieces he removes first. After rearrangement the center line doesn’t quite line up the the right side of the smaller pieces anymore.

What is your solution?

-David Drumm (Nal)

## 11 thoughts on “Impossible Puzzle”

1. DigitalDave says:

Notice in the “performance” that the interlocking small pieces are tightly wedged in for the 2nd arrangement, but very loose for the 3rd.

Also note how the large piece must be held still by the free hand when going into the 3rd arrangement, lest the camera show how loosey-goosey that piece fits into its alloted space — it would have slided and turned easily when bumped otherwise.

This is what’s know as “sleight of hand”.

2. I am puzzled by this puzzle??? Wasn’t Rubic’s Cube bad enough for mere mortals like myself?

3. JoshOnPC says:

Byron,

Being as all the pieces are of fixed surface areas, there are no concievable arrangements of all the pieces which would produce a different total surface area. It therefore must be that the pieces either fill the entire area of the rectangle in which they lie, or they don’t. It can not be both. Since in one example they clearly do not, it must be that the extra space is hidden in the gaps of the first arrangement.

4. Nal says:

Thanks Paul. A more interesting problem than I had originally considered.

5. PaulThomson says:

This is called the “Missing Square” puzzle. There are many variations on it.

6. Byron says:

Tony C:

no, they really do fit but the angle and proportion of the pcs is important to achieve that space when rearranged. The boundary lines have nothing to do with it. It’s just trigonometry. At least in my opinion.

7. Tony C. says:

@Byron: Yeah, when the pieces don’t *really* fit together, the gaps created look like thicker boundary lines, which we are taught to ignore but are actually deceptive in this case. We are saying the same thing; the pieces don’t really fit. The angled lines are (psychologically speaking) the best place to “hide” the extra space.

8. Byron says:

I drew that thing in cad with 0 width for boundaries and it appears to do with the angle of the triangle above. and also the pieces have to be just the right proportion which I was unable to duplicate. I drew it several different ways and they all gave me additional depth or reduced width. It doesn’t have, at least in my opinion, anything to do with the boundary lines but with the angle of the triangle and the proper proportioning of the pieces.

9. Carlyle Moulton says:

Tony C.

I think you have it, but I think the video is dishonest by being at a scale that hides the fact that in the space filling arrangement the pieces do not fit cleanly together.

10. Tony C. says:

There are several variants on this all depending on the same thing; what you mentioned: The pieces do not fit perfectly. Notice how the arrangement with the extra space fits tightly enough to make the boundary lines almost disappear, while the “space filling” version has clear dark boundary lines. It actually relies on something we are taught since kindergarten: That lines are boundaries and should be presumed to have zero width! In geometry, drawing, on architectural plans and maps and more, we are taught (mostly implicitly) that a thin dark line around an object indicates a boundary; not a real thing you expect to see. If a child draws an apple and colors it red, the black pencil line is not something they expect to see around real apples.

In this case, the slight gaps between pieces in the “space filling” version do not admit enough light to see the yellow background, but are still there.