A company makes charm bracelets with 4 charms: A, B, C, and D. There are 24 different orders they can enter the machine:
ABCD ABDC ACBD ACDB ADBC ADCB
BCAD BCDA BDAC BDCA CABD CADB
CDAB CDBA DABC DACB DBAC DBCA
BACD BADC CBAD CBDA DCAB DCBA
Once the charms are threaded on a bracelet many of the arrangements look the same. If the relation R on the set S of line arrangements with the rule (X,Y) ∈ R if arrangements X and Y look the same when threaded on a bracelet, what is the partition of the set S induced by R?
Would this be right?
The partition of the set S induced by R is {{ABCD, BCDA, CDAB, DABC}, {ABCD, BDCA, DCAB, CABD}, {ACBD, CDBA, DBAC, BACD},{ADBC, DBCA, BCAD, CADB}, {ADCB, DCBA, CBAD, BADC}}
Almost. Note that you can flip around a bracelet.
... or would a bracelet and its flipped counterpart not 'look the same'? Then again, if I rotate a bracelet, one could argue that that does not look the same either ... Hmmm ... maybe you shpould look for some clarification on what 'look the same' exactly means ...
(BTW: you're missing $4$ orders... Also, first entry of second set should be ABDC, and first entry of third set ACDB...)