Solution. This is similar to the example above

This is similar to the example above. As with the example above the answer needs to be divided by 4 because of the repetitions caused by the fact that it is on a circle. However in this situation there is another constraint because the necklace can be turned over giving an equivalent answer. In the diagrams below, these two situations are actually the same, but appear as two separate permutations of the answer.

Hence we need to divide the answer by 2.

Therefore the number of permutations is .