Is there a solution for a straight-bar piece not touching the edge of the rectangle? By rectangle solution, I mean either one of the patterns 15x4, 12x5, or 10x6. By straight-bar piece, I mean the piece of 5 stones in a straight row. Literate pentomino crackers denote this piece with the letter "I".
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1 Answer
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Here's one solution for the $10{\times}6$ rectangle:
Here are all $11$:
vvvllllzzy
viiiiilzyy
vxffwwzzny
xxxffwwtny
uxufppwtnn
uuuppptttn
vvvllllzzn
viiiiilznn
vxffwwzzny
xxxffwwtny
uxufppwtyy
uuupppttty
yzzllllvvv
yyzliiiiiv
ynzzwwxffv
yntwwxxxff
nntwppxufu
ntttpppuuu
nzzllllvvv
nnzliiiiiv
ynzzwwxffv
yntwwxxxff
yytwppxufu
ytttpppuuu
tnnnllllpp
tttnnfflpp
tiiiiiffxp
vvvzwwfxxx
vzzzywwuxu
vzyyyywuuu
wwtttxffuu
pwwtxxxffu
ppwtyxzfuu
ppyyyyzzzv
liiiiinnzv
llllnnnvvv
pptttxffuu
ppwtxxxffu
pwwtyxzfuu
wwyyyyzzzv
liiiiinnzv
llllnnnvvv
wwfftttxuu
pwwfftxxxu
ppwfytzxuu
ppyyyyzzzv
liiiiinnzv
llllnnnvvv
ppfftttxuu
ppwfftxxxu
pwwfytzxuu
wwyyyyzzzv
liiiiinnzv
llllnnnvvv
uuxfftttpp
uxxxfftwpp
uuxzfytwwp
vzzzyyyyww
vznniiiiil
vvvnnnllll
uuxfftttww
uxxxfftwwp
uuxzfytwpp
vzzzyyyypp
vznniiiiil
vvvnnnllll
There is only one solution for the $12{\times}5$ rectangle:
llllnnnffppp
liiiiinnffpp
vzyyyywtfxuu
vzzzywwtxxxu
vvvzwwtttxuu
There are no solutions for the $15{\times}4$ rectangle.
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$\begingroup$ The 11 solutions for 10x6 can be grouped into 3 classes: the first four are generated by flipping NY and/or FX from one of them, the 5th is unique, and the other 6 are generated by flipping WP and/or permuting XFT. $\endgroup$– BubblerCommented Jul 8 at 1:23