The problem of arranging copies of a polyomino to form a rectangle
has been studied for a long time.
The problem of arranging copies of two polyominoes to form a rectangle
was studied by Earl Kramer and Frits Göbel in Tiling Rectangles
with Pairs of Pentominoes,
Journal of Recreational Mathematics
16(3) (1983), 198–206.
Later it was studied in Rodolfo Kurchan's Puzzle Fun,
Issue 19,
Tyling with Pairs of Polyominoes.
Still later, the problem was studied
further in Erich Friedman's Math Magic for August 2010.
Here I study the problem of arranging copies of three pentominoes to form a rectangle, using at least one of each.
Carl Schwenke and Johann Schwenke improved on one of my solutions.
See also Three-Pentomino Balanced Rectangles.
FIL 4 | FNV 6 | FUZ 5 | INU 5 | IUY 3 | LPV 3 | LWZ 6 | NVW 8 | PVX 6 | TXZ — |
FIN 11 | FNW — | FVW 10 | INV 4 | IUZ 7 | LPW 4 | LXY 6 | NVX 14 | PVY 3 | TYZ 6 |
FIP 4 | FNX — | FVX 15 | INW 9 | IVW 7 | LPX 6 | LXZ 8 | NVY 5 | PVZ 3 | UVW 30 |
FIT 10 | FNY 5 | FVY 5 | INX 19 | IVX 24 | LPY 3 | LYZ 5 | NVZ 3 | PWX 6 | UVX 4 |
FIU 3 | FNZ — | FVZ 5 | INY 5 | IVY 4 | LPZ 3 | NPT 3 | NWX — | PWY 3 | UVY 3 |
FIV 5 | FPT 4 | FWX — | INZ 7 | IVZ 3 | LTU 5 | NPU 3 | NWY 7 | PWZ 4 | UVZ 5 |
FIW 11 | FPU 3 | FWY 6 | IPT 3 | IWX 20 | LTV 4 | NPV 3 | NWZ — | PXY 5 | UWX 23 |
FIX 15 | FPV 4 | FWZ — | IPU 3 | IWY 5 | LTW 5 | NPW 5 | NXY 7 | PXZ 6 | UWY 4 |
FIY 5 | FPW 5 | FXY 7 | IPV 3 | IWZ 7 | LTX 8 | NPX 6 | NXZ — | PYZ 4 | UWZ — |
FIZ 15 | FPX 8 | FXZ — | IPW 4 | IXY 6 | LTY 4 | NPY 3 | NYZ 6 | TUV 5 | UXY 5 |
FLN 5 | FPY 4 | FYZ 5 | IPX 5 | IXZ 15 | LTZ 5 | NPZ 4 | PTU 4 | TUW 15 | UXZ 23 |
FLP 3 | FPZ 4 | ILN 3 | IPY 3 | IYZ 6 | LUV 5 | NTU 4 | PTV 3 | TUX 17 | UYZ 5 |
FLT 6 | FTU 5 | ILP 3 | IPZ 3 | LNP 3 | LUW 6 | NTV 5 | PTW 4 | TUY 5 | VWX 57 |
FLU 3 | FTV 10 | ILT 3 | ITU 7 | LNT 4 | LUX 3 | NTW 11 | PTX 6 | TUZ 16 | VWY 5 |
FLV 4 | FTW 14 | ILU 4 | ITV 6 | LNU 4 | LUY 3 | NTX 11 | PTY 3 | TVW 5 | VWZ 8 |
FLW 5 | FTX — | ILV 3 | ITW 7 | LNV 4 | LUZ 5 | NTY 5 | PTZ 5 | TVX — | VXY 8 |
FLX 8 | FTY 6 | ILW 4 | ITX 17 | LNW 6 | LVW 5 | NTZ 11 | PUV 4 | TVY 5 | VXZ 21 |
FLY 5 | FTZ — | ILX 6 | ITY 5 | LNX 6 | LVX 8 | NUV 6 | PUW 5 | TVZ 6 | VYZ 4 |
FLZ 4 | FUV 3 | ILY 3 | ITZ 10 | LNY 4 | LVY 4 | NUW 7 | PUX 3 | TWX 20 | WXY 9 |
FNP 4 | FUW 4 | ILZ 5 | IUV 7 | LNZ 5 | LVZ 3 | NUX 7 | PUY 3 | TWY 7 | WXZ — |
FNT 10 | FUX 5 | INP 3 | IUW 11 | LPT 3 | LWX 9 | NUY 4 | PUZ 4 | TWZ 14 | WYZ 6 |
FNU 4 | FUY 3 | INT 6 | IUX 4 | LPU 3 | LWY 5 | NUZ 8 | PVW 4 | TXY 9 | XYZ 7 |
Last revised 2024-02-28.