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My initial findings Friday were that when comparing the {4,3,3} 3 as is,
there would be twice as many possible states if you allow more non-3D face
twists (specifically 3x3x1x1 twists), and yet, it should make it an easier
puzzle.
As is, I calculate 2152*377*514*79*115*134*172*192*232*29*31 possible
states,
or if the html breaks down: 2^152 * 3^77 * 5^14 * 7^9 * 11^5 * 13^4 * 17^2 *
19^2 * 23^2 * 29 * 31
, but with the other twists added the only change is that the 2^152 goes to
2^153. When I use calc to compute them I get around 1.75*10^120 and
3.5*10^120 possible states respectively.
The difference is from 16!/2 ways of currently placing the 4C pieces.but
with the other twists added there are 16! ways of placing the 4C pieces. To
refresh everyone on the '!' symbol, 7! = 7*6*5*4*3*2*1.
Similarly for the {4,3,3} 2: there are twice as many states if you allow
2x2x1x1 twists.
currently 240*320*53*72*111*131 possible states
= 2^40 * 3^20 * 5^3 * 7^2 * 11^1 * 13^1
the only change is that 2^40 goes to 2^41 for the exact same 4C reason.
This makes for 3.36*10^27 and 6.72*10^27 possible states respectively.
--
Andy
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osoft-com:office:office" xmlns:w=3D"urn:schemas-microsoft-com:office:word" =
xmlns:m=3D"http://schemas.microsoft.com/office/2004/12/omml" xmlns=3D"http:=
//www.w3.org/TR/REC-html40">
My initial findings Friday were that when com=
paring
the {4,3,3} 3 as is, there would be twice as many possible states if you al=
low
more non-3D face twists (specifically 3x3x1x1 twists), and yet, it should m=
ake
it an easier puzzle.
As is, I calculate 2152*377<=
/sup>*514*79*115*134*172sup>*192*232*29*31
possible states,
or if the html breaks down: 2^152 * 3^77 * 5=
^14 *
7^9 * 11^5 * 13^4 * 17^2 * 19^2 * 23^2 * 29 * 31
, but with the other twists added the only c=
hange
is that the 2^152 goes to 2^153. When I use calc to compute them I ge=
t
around 1.75*10^120 and 3.5*10^120 possible states respectively.
/p>
The difference is from 16!/2 ways of current=
ly
placing the 4C pieces…but with the other twists added there are 16! w=
ays
of placing the 4C pieces. To refresh everyone on the '!' symbol, 7! =
=3D 7*6*5*4*3*2*1.
Similarly for the {4,3,3} 2: there are=
twice
as many states if you allow 2x2x1x1 twists.
currently 240*320*5
possible states
=3D 2^40 * 3^20 * 5^3 * 7^2 * 11^1 * 13^1
the only change is that 2^40 goes to 2^41 fo=
r the
exact same 4C reason. This makes for 3.36*10^27 and 6.72*10^27 possib=
le
states respectively.
--
Andy