Just six different rings may be formed without breaking the conditions.
Here is one way of effecting the arrangements.
A B C D E F G H I J K L M
A C E G I K M B D F H J L
A D G J M C F I L B E H K
A E I M D H L C G K B F J
A F K C H M E J B G L D I
A G M F L E K D J C I B H
Join the ends and you have the six rings.
Lucas devised a simple mechanical method for obtaining the _n_ rings that
may be formed under the conditions by 2_n_+1 children.