# Separated Pentominoes Tiling a Rectangle

## Introduction

In Issue #25 of Puzzle Fun, Rodolfo Marcelo Kurchan asked which rectangles can be tiled with a given set of 3 or 4 pentominoes, not letting like pentominoes touch, even at corners. Here I show the largest known such rectangles.

Corrections are welcome.

## 3 Pentominoes

### No Solution

 FIL FIN FIP FIT FIU FIV FIW FIX FIY FIZ FLN FLT FLU FLV FLW FLX FLY FLZ FNP FNT FNU FNV FNW FNX FNY FNZ FPT FPV FPW FPX FPZ FTU FTV FTW FTX FTY FTZ FUV FUW FUX FUY FUZ FVW FVX FVY FVZ FWX FWY FWZ FXY FXZ FYZ ILV ILW ILX ILY ILZ INP INT INU INW INX INY INZ IPU IPV IPW IPX ITU ITV ITW ITX ITY ITZ IUV IUW IUY IUZ IVW IVX IVY IWX IWY IWZ IXY IXZ IYZ LNT LNU LNW LNX LNY LPU LPX LTU LTV LTW LTX LUV LUW LUY LUZ LVW LVX LVY LVZ LWX LWY LWZ LXY LXZ NPT NPW NPX NPZ NTU NTV NTW NTX NTY NTZ NUV NUW NUX NUY NUZ NVW NVX NVY NVZ NWX NWY NWZ NXY NXZ NYZ PTU PTV PTX PTY PTZ PUW PUX PVW PVX PWX PXY PXZ TUV TUW TUX TUZ TVW TVX TVY TVZ TWX TWY TWZ TXY TXZ TYZ UVW UVX UVY UVZ UWX UWY UWZ UXY UXZ UYZ VWX VWY VWZ VXY VXZ VYZ WXY WXZ WYZ XYZ

### Infinite Solutions

 FPU ILT ILU IPT IPZ IUX IVZ LNP LNV LPT LPV LPY LPZ LTY NPU NPY PTW PUV PUY PVY PVZ PWZ PYZ

## 4 Pentominoes

### No Solution

 FILW FILX FINX FINZ FIPX FITU FITV FITW FITZ FIUX FIUZ FIVW FIVY FIVZ FIWX FIWY FIWZ FIXY FIXZ FIYZ FLVW FLVX FLWX FLXY FLXZ FNPX FNTW FNTX FNUW FNUX FNVW FNVX FNVZ FNWX FNWZ FNXZ FPTX FPTZ FPWX FPXZ FTUW FTUX FTUZ FTVW FTVX FTVZ FTWX FTWZ FTXY FTXZ FTYZ FUVW FUVX FUWX FUWZ FUXZ FVWX FVWZ FVXZ FWXY FWXZ FXYZ ILNX ILTW ILTX ILUW ILUZ ILVW ILVX ILWX ILWZ ILXY ILXZ INTU INTV INTZ INUW INUX INVW INVX INWX INWZ INXZ IPTX IPWX ITUV ITUW ITUX ITUZ ITVW ITVX ITVZ ITWX ITWY ITXY ITXZ ITYZ IUVW IUVX IUWX IUWZ IUXY IUXZ IVWX IVWZ IVXY IVXZ IVYZ IWXY IWXZ IXYZ LNVX LNWX LNWZ LNXZ LTUW LTUX LTVW LTWX LTWY LTWZ LTXY LTXZ LUVW LUWX LUWZ LVWX LVWZ LVXY LVXZ LWXY LWXZ NPTX NPWX NPXZ NTUV NTUW NTUX NTVW NTVX NTWX NTWZ NTXY NTXZ NUVW NUVX NUWX NUWZ NUXZ NVWX NVWZ NVXY NVXZ NWXY NWXZ NXYZ PTWX PTXZ PVWX PVXZ PWXZ TUVW TUVX TUVZ TUWX TUWZ TUXZ TUYZ TVWX TVWY TVWZ TVXY TVXZ TVYZ TWXY TWXZ TXYZ UVWX UVWY UVWZ UVXY UWXY UWXZ UXYZ VWXY VWXZ WXYZ

### Infinite Solutions

 FILN FILP FILT FILU FILY FILZ FINP FINY FIPT FIPU FIPV FIPW FIPY FIPZ FITX FITY FIUY FLNP FLNT FLNU FLNV FLNW FLNY FLNZ FLPT FLPU FLPV FLPW FLPX FLPY FLPZ FLTU FLTV FLTW FLTX FLTY FLTZ FLUV FLUW FLUY FLUZ FLVY FLVZ FLWY FLYZ FNPT FNPU FNPV FNPW FNPY FNPZ FNTU FNTV FNTY FNTZ FNUV FNUY FNUZ FNVY FNWY FNXY FNYZ FPTU FPTV FPTW FPTY FPUV FPUW FPUX FPUY FPUZ FPVW FPVY FPVZ FPWY FPWZ FPXY FPYZ FTUV FTUY FTVY FTWY FUVY FUWY FUXY FUYZ FVYZ FWYZ ILNP ILNT ILNU ILNV ILNW ILNY ILNZ ILPT ILPU ILPV ILPW ILPX ILPY ILPZ ILTU ILTV ILTY ILTZ ILUV ILUX ILUY ILVY ILVZ ILWY ILYZ INPT INPU INPV INPW INPY INPZ INTX INTY INUV INUY INUZ INVY INVZ INWY INYZ IPTU IPTV IPTW IPTY IPTZ IPUV IPUW IPUY IPUZ IPVW IPVY IPVZ IPWY IPWZ IPXZ IPYZ ITUY ITWZ IUVY IVWY IWYZ LNPT LNPU LNPV LNPW LNPX LNPY LNPZ LNTU LNTV LNTX LNTY LNTZ LNUV LNUW LNUX LNUY LNUZ LNVY LNVZ LNWY LNYZ LPTU LPTV LPTW LPTX LPTY LPTZ LPUV LPUW LPUX LPUY LPUZ LPVW LPVX LPVY LPVZ LPWX LPWY LPWZ LPXY LPXZ LPYZ LTUV LTUY LTVY LTVZ LTYZ LUVX LUVY LUVZ LUWY LUXY LUYZ LVWY LVYZ LWYZ LXYZ NPTU NPTV NPTW NPTY NPTZ NPUV NPUW NPUX NPUY NPUZ NPVW NPVY NPVZ NPWY NPWZ NPXY NPYZ NTUY NTUZ NTVY NTVZ NTWY NTYZ NUVY NUWY NUYZ NVWY NVYZ NWYZ PTUV PTUW PTUX PTUY PTUZ PTVW PTVY PTVZ PTWY PTWZ PTYZ PUVW PUVX PUVY PUVZ PUWY PUWZ PUXY PUXZ PUYZ PVWY PVWZ PVXY PVYZ PWXY PWYZ PXYZ TUVY TUWY TWYZ UVXZ UWYZ VWYZ

### Largest Known Rectangles

Last revised 2022-09-04.

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Col. George Sicherman [ HOME | MAIL ]