x is one colour and o is another
I found that I could make 6 patterns with my 8 blocks
xxoo ooxx
xoxo oxox
xoox xoox
oxxo oxxo
ooxx xxoo
oxox xoxo
I found that I could make only 6 patterns with my 9 blocks
xxoo o ooxx
xoxo o oxox
xoox o xoox
oxxo o oxxo
ooxx o xxoo
oxox o xoxo
One colour has to be in the middle every time because one group is an odd number and can't be halved to make the necklace symmetrical
I found that I could not a pattern with 10 block if I had 5 of each because if you have an odd number it has to go in the middle and you can't do that with two.
I found that I could only make only neckalaces with 10 beads if you had even numbers of each colour 2 and 8, 4 and 6, 6 and 4, 8 and 2 and [10 and 0 - not really two colours]
With 6 and 4 blocks I can make 10
On each side there is
xxooo
oxxoo
ooxxo
oooxx
xoxoo
oxoxo
ooxox
xooxo
oxoox
xooox