Using the same pieces in the same frame, the video shows a gridded tile design assembled with 10-pieces occupying the same area as 8-pieces.
Apologies for my poor video compression results … couldn’t find any discussion on maximum upload file size allowed.
What the eye sees are two 2D packings where the same area is covered with fewer tile pieces. Shown is my simplified version of this puzzle originally presented by magician Winston Freer. The magic is in 3D packing…
Using the same geometry but no scored grid, the photos show assemblies with total number of pieces 10, 9, 8, and 7 that all fit in the same frame.
Notice the second case is a bit looser than the first. Very careful measurement and if you concentrated all that looseness is exactly equal to the nonfitting pieces.
Using those large pieces at the top makes the gap less noticeable
Piece #2 is flipped over. If you watch the video carefully, you will note the flipping. It’s the same piece, just flipped to put its bevel on the bottom of the piece rather than at the top where it slips under the bevel on part #1. The expanded area resulting from this change in 3D packing is exactly equal to the area of squares 9 and 10, by design. So the 8-piece assembly should exactly fit the original frame size assuming there were no kerfs. The 9-piece and 7-piece assemblies have slightly smaller heights.
Should have used MDF which would have homogeneous surface texture on both sides.
This is the original Freer design, I believe. Bevels are used on all slanted edges. I simplified by using bevels on only two edges at the expense of making the bevels more obvious. But bevels are nasty to make.
By the way, the bevel area can be designed to exactly accommodate one, two, or three missing pieces. The smaller the bevel area, the less obvious it is to notice. But the fit in the frame should be exact in each case.
Using art-work non-kerfed dimensions, the inside height of the frame is 5.000 inches. The ten-piece assembly height is 5.000 inches. The eight-piece height is 5.000 inches. The nine-piece height is 4.946 inches. The seven-piece height is 4.945 inches. If there were no kerfing and perfect beveling, the looseness would be less noticeable.
