We haven't addressed Mike Stay's question, which stymies me also: "Clearly the puzzle involves placing the pieces at an angle, but exactly which angle and how to arrange the pieces is the hard problem. Are there algorithms for solving a puzzle like this other than brute force?" For example, "Four Fit" a/k/a "Martin's Menace", Stewart Coffin's design #217, has a target area that can also be filled with various other sets of 4 pentominoes. Eliminating those that fill a grid-aligned a 4x5 (contained in the Four Fit box), there are 56; arbitrarily ignoring those that have duplicate pieces leaves 21 sets (including the original FTYZ): FLNP FNXZ LTYZ FLNT FPTU LUYZ FLPT FPVW LVYZ FNPT FPWY NPTZ FNPU FTVZ NPUZ FNPZ FTYZ NPYZ FNTZ LNPY PVYZ Four Z pentominoes make an alternate target area: A B B A A A B A C C B B D C D D D C C D The above has a tilted bounding box of side 22/sqrt(17) = ~5.33578, area 484/17 = ~28.47059 < 28.6 = Four Fit target area. Four Z's do not seem to fit in the 22/sqrt(17) box in any other way, BUT my ability to find weird packings is poor. Closely related to M Stay's question is whether any of the other 20 sets above, or the four Z's in the smaller box, have only the compact trick solution. I don't know of any way but very messy brute force. Any ideas? -- Mike Beeler