I have 4 marbles coloured Red, Green, Blue, Yellow.
I have a board of 16 cells comprising 4 subcells of 2 by 2 in which my marbles R,G,B,Y must (all) be placed.
The added constraint is that each marble must occupy the same relative position in all four subcells of the table so that
R=TopLeft, G =TopRight
Y=BottomLeft, Blue=BottomRight
This means that
RG xx
YB xx
xx xx
xx xx
and
Rx xG
Yx xB
xx xx
xx xx
and
xx xx
xB Yx
xG Rx
xx xx
Are legal positions. But
GY xx
xx xx
BR xx
xx xx
Or
xx xx
xR Yx
xG Bx
xx xx
are not legal positions.
So the question is - how many legally filled tables do I have here? And how do I extend this to bigger tables, and larger colour sets?
Thanks in advance!
P
I have a board of 16 cells comprising 4 subcells of 2 by 2 in which my marbles R,G,B,Y must (all) be placed.
The added constraint is that each marble must occupy the same relative position in all four subcells of the table so that
R=TopLeft, G =TopRight
Y=BottomLeft, Blue=BottomRight
This means that
RG xx
YB xx
xx xx
xx xx
and
Rx xG
Yx xB
xx xx
xx xx
and
xx xx
xB Yx
xG Rx
xx xx
Are legal positions. But
GY xx
xx xx
BR xx
xx xx
Or
xx xx
xR Yx
xG Bx
xx xx
are not legal positions.
So the question is - how many legally filled tables do I have here? And how do I extend this to bigger tables, and larger colour sets?
Thanks in advance!
P