Statistics

Problem Statement for "DistinctDice"

Problem Statement

Let's consider a standard six-sided die. Each side contains a distinct number between 1 and 6. We can represent a single die as a sequence of 6 digits in the following order: the number on its top side, bottom side, left, right, front and back sides. You are given a String[] givenDice, each element of which represents a single die in the described format.

Your task is to determine the number of distinct dice in givenDice. Two dice are considered equal if they can be rotated in such a way that the numbers on the corresponding sides are all equal.

Definition

Class:
DistinctDice
Method:
getDistinct
Parameters:
String[]
Returns:
int
Method signature:
int getDistinct(String[] givenDice)
(be sure your method is public)

Constraints

  • givenDice will contain between 1 and 50 elements, inclusive.
  • Each element of givenDice will contain exactly 6 characters.
  • Each character of each element of givenDice will be a digit between '1' and '6', inclusive.
  • Within each element of givenDice, all characters will be distinct.

Examples

  1. {"123456","654321"}

    Returns: 1

  2. {"145326","154236","216543"}

    Returns: 3

  3. {"165324"}

    Returns: 1

  4. {"145362","254613","216543"}

    Returns: 3

  5. {"546231", "245631", "531462", "524631", "614235", "415623", "423651", "316254", "432165", "316452", "135426", "643512"}

    Returns: 10

  6. {"142653","412536","465123","415632","136452","563421","325416","632514","652314","643512","456132","614532","356124","514326"}

    Returns: 13

  7. {"365421","362514","251346","354126","432651","354162","625314","513246","126435","643152","436125","654213","243615","643521","146532"}

    Returns: 13

  8. {"413256","265143","546132","234615","154362","361245","234156","235614","314625","615423","613542","562341","342561","321564","126345","126435"}

    Returns: 10

  9. {"163452","423615","261435","125643","623415","143265","354216","436251","546213","126543","624351","462315","365421","653421","512463","152436","564231"}

    Returns: 14

  10. {"342165","132645","623145","132654","453216","314652","453261","654231","345216","364125","156432","136425","534216","412356","143625","526314","235461","325416"}

    Returns: 14

  11. {"214653","152463","216453","145236","461532","345126","351426","513246","426513","254136","152346","124536","243156","542631","312456","125643","354126","156324","134625"}

    Returns: 17

  12. {"541632","431562","635124","265431","563412","135624","643125","361452","462153","534162","416253","243156","435126","432165","421365","531462","534261","364125","354261","351624"}

    Returns: 15

  13. {"123456","132546","145326","154236","216543","245163","254613","261453","316452","345612","354162","361542","416235","423615","432165","461325","516324","523164","532614","561234","623541","632451","645231","654321"}

    Returns: 4

  14. {"413625","416523","325461","265134","461352","243615","324561","615243","543216","143526","426531","156423","261345","312546","254613","642135","462153","546321","541263","456231"}

    Returns: 15

  15. {"651423","642135","162453","261435","316542","624153","643512","326154","142356","653241","625314","351462","531462","541362","162543","526413","346125","245631","453162","136245","165342","536214"}

    Returns: 13

  16. {"643125","134562","456213","542361","216345","312654","625431","314652","536412","325461","124356","623145","216435","614532","235416","451362","142653","314256","346251","536241","235641","563214","541632","512634"}

    Returns: 16

  17. {"351246","136452","425361","521463","641523","315246","542613","361245","236514","256134","316542","561342","143256","324561","364521","145236","523146","461235","514632","546321","365421","534126","362145","234615","213465","643215"}

    Returns: 18

  18. {"514623","142635","452316","526134","514326","125346","215463","352461","416523","631245","246513","215364","546123","452163","564321","462153","543261","642531","352164","314652","134562","326541","521346","513264","361542","412365","146253","462315"}

    Returns: 19

  19. {"132564","523461","231546","253146","364215","513264","326415","542136","543216","234561","634251","316254","526341","641325","142365","261435","243615","213546","365412","512643","324651","623541","541326","453261","534261","324165","316524","251463","462153","243156"}

    Returns: 22

  20. {"352614","134265","154263","653421","462531","316542","246315","652314","421536","154623","651234","462153","124635","321645","354126","324516","241635","452631","432651","514632","312546","623451","164352","546312","213654","342561","316524","251634","653214","216345","463215","562314"}

    Returns: 24

  21. {"214635","645213","362451","653214","316524","653412","152364","364512","436251","612435","512634","312654","521364","516324","365412","613524","651423","416532","365421","412356","143256","134562","561432","365142","154362","341625","421635","136425","643521","453612","512346","342156","532641","563214"}

    Returns: 20

  22. {"465321","532461","356241","123456","426135","615432","364152","263154","214365","263514","415236","362145","261354","124536","412365","126543","153462","265143","263415","652314","364215","423615","416523","631524","513642","216354","241635","265341","125436","546321","524613","432651","246153","263541","341526","245613"}

    Returns: 20

  23. {"631542","314625","512643","536142","243615","154236","146235","164532","216435","164523","532416","236145","124356","231456","162453","256143","643512","654123","354621","452613","132465","564231","642513","254631","453126","231564","361254","413265","631245","214653","316245","165324","251463","542163","231546","625341","634215","461235"}

    Returns: 24

  24. {"451623","142653","563421","623154","341562","542136","561234","253641","243561","453126","634251","463521","261354","563412","536142","432516","325641","623415","152463","243165","645321","215643","546231","456213","521364","246315","523641","513642","524136","354612","125463","651234","532146","426351","645312","245163","613452","213465","265413","342165","251436","541632","562413","415362","152346","534162","243615","624351","364152","416325"}

    Returns: 23

  25. {"542361","246315","534126","314652","435261","536241","162543","136542","145326","346512","642513","352641","245613","651243","365412","564312","256314","623415","651342","453261","416352","342516","643512","416523","436152","653142","623154","125436","165342","561234","452631","124563","123645","524361","512643","214365","612354","642153","453612","123456","415632","562341","241653","645312","436125","461235","536142","251346","531642","431265"}

    Returns: 25

  26. {"321456","431625","235614","341562","654231","562314","526314","625341","624531","641523","413265","526413","612534","345162","514326","241536","231564","164523","415362","426531","254613","361524","324561","645123","246513","325641","314625","351462","524136","261453","261345","216345","163542","461523","142356","516324","126453","251643","561423","152634","521436","654312","125463","534261","436512","654213","432615","264513","423561","635412"}

    Returns: 27

  27. {"526134","536142","423156","261534","415326","162435","415623","413265","165342","216534","523416","426135","245613","536241","243615","213654","345216","235164","426153","312465","432156","135462","463521","126354","462153","145326","324651","451362","156423","432561","351246","235146","315426","563142","456213","145236","561432","132546","214653","123546","152364","341256","263154","235614","246153","541632","642351","463152","435126","653142"}

    Returns: 24

  28. {"625143","431562","135624","351246","263154","145236","534621","425361","243561","142653","564213","621453","356214","452361","623514","236541","412356","156432","436521","641352","124356","523164","543126","654231","325146","463251","514623","613245","152346","146352","142563","546312","421536","451236","526341","132645","254631","153426","243615","631542","416352","634125","315426","365214","214536","561423","125364","564123","364251","153246"}

    Returns: 25

  29. {"641352","462513","542316","516234","213456","635214","651234","215643","354162","465213","312654","465312","364215","356412","524163","465132","423651","254136","325164","512346","312546","264513","423615","532146","145362","524361","521634","653142","341562","534126","516324","563241","154362","162435","325146","543216","563142","652431","156243","321654","435126","432651","254613","136245","162534","231654","562314","654123","412536","624315"}

    Returns: 26

  30. {"164352","361542","546123","265431","652134","614523","516423","634152","243651","512436","452631","342615","561432","463125","214653","216345","241635","534216","362415","431625","614352","326514","346125","361524","265143","452361","654231","135246","352461","463215","124653","132546","624531","164325","251346","354261","356421","431265","541623","341526","416352","516243","426315","463521","236514","461253","152346","641235","642513","615324"}

    Returns: 25

  31. {"165423","536412","456123","365421","163254","526431","354126","641253","132546","421356","315264","425613","436215","352614","165432","213654","351624","153624","431562","236514","541236","643152","562314","241635","641532","635241","453261","356124","216435","231564","356421","432165","651423","316542","346521","416532","215634","245163","462315","621345","413625","265143","345612","423156","256143","241536","436521","615423","145632","423165"}

    Returns: 25

  32. {"316542","215463","154632","561234","163425","324561","354612","145362","321654","342561","625134","523614","231456","523641","534126","361524","632451","265143","135462","612345","652314","246315","261543","256431","154326","312465","613524","126453","164532","462153","546312","614235","254631","356124","541632","641253","264513","415236","143625","256314","126543","514326","251346","132564","145263","623415","621354","421356","621543","536241"}

    Returns: 28

  33. {"463152","152346","123546","516243","534261","425613","264135","264513","425631","461325","265143","413526","635124","364125","521364","452136","436125","624513","214356","413652","324615","125634","134652","635412","264315","134625","364152","532614","651234","452361","653421","145632","256143","245136","124365","362154","253461","432561","524631","326145","623154","253641","654123","326154","541623","354162","214563","412563","426153","265134"}

    Returns: 25

  34. {"345162","563124","245316","536142","265143","526143","142635","245613","546132","431652","251463","523641","135246","314625","641523","642531","614325","463512","542361","325614","125436","246135","162354","532641","516432","524361","651432","135624","521346","523164","425163","251634","542136","416253","514623","531426","463125","631524","614235","635124","653142","361452","412653","316425","523416","621345","512364","345216","342516","234561"}

    Returns: 24

  35. {"624135","631425","532146","124653","452136","625134","241653","641532","541632","132546","213654","265143","563421","523614","142365","623514","431526","312465","362145","541263","352614","361542","562431","234615","423651","342156","152463","426135","631452","516432","432651","134526","153264","635421","514362","641325","612534","356241","354126","614235","456231","132465","645213","426315","413265","643125","125436","243561","564123","415263"}

    Returns: 23

  36. {"642153","562431","526143","435162","315642","154236","236451","235461","153246","136254","523146","435612","362541","465321","145326","241563","362154","254163","543126","624135","354126","134625","541362","136524","146325","215463","346251","563412","124653","142653","453612","134652","256143","412563","136425","546213","534261","462513","623514","165342","456231","251634","162354","652413","452316","325614","264135","235164","231456","143256"}

    Returns: 27

  37. {"253461","465123","236154","416253","246513","421653","342561","346125","356142","641523","463251","241536","425361","413526","145263","321654","624513","564321","562431","651423","642513","315264","621345","645213","314265","164325","214365","614532","235461","514236","132546","125634","154362","543216","324651","263514","536412","412563","634152","425631","562341","631425","561432","614235","625134","341265","643512","241635","356214","231546"}

    Returns: 26

  38. {"432615","643215","241653","512346","642351","246513","413526","425136","351264","523641","641325","561342","512436","251346","125463","325146","523146","435612","164325","132465","341625","153642","634215","152643","346215","614352","643152","132645","514623","352614","152463","642135","213456","634125","346512","542136","415236","651243","132654","435126","631524","463125","321456","325164","125634","126354","536124","431256","123456","614253"}

    Returns: 22

  39. {"126345","241635","346152","234516","462531","162435","536421","152346","134652","645213","126534","135426","235416","516234","532641","321564","435261","634125","516324","125436","514263","134625","146352","263415","453216","625314","451263","163425","532416","562134","451326","314625","412536","235164","416325","213645","256314","465231","524163","254163","361254","416235","142635","415236","145362","261543","423165","354162","152643","462315"}

    Returns: 24

  40. {"634521","621345","635142","245613","231645","526143","526431","561324","341526","652413","241635","513426","543612","351264","236154","416253","523416","326154","415623","241563","456231","543621","145632","324516","613524","134265","623451","312546","651432","651324","135426","512634","362514","461523","324615","456123","132465","416352","532614","251643","423561","234561","316542","423615","362451","462135","625143","124653","521436","612534"}

    Returns: 26

  41. {"415236","314265","152364","543126","146352","635241","546231","412653","465132","563241","251364","163524","465321","461532","534261","146532","253641","514263","234651","351264","625341","134265","352641","325614","436152","536214","456213","342156","624153","356124","635412","456123","621354","314625","625413","236145","352164","345126","654312","142635","263541","632145","623451","412635","231654","165234","162453","516234","153462","342651"}

    Returns: 26

  42. {"214653","624351","251634","431256","261435","523146","142356","146352","514326","426351","452316","154632","146253","261453","612345","623514","541623","563421","216453","524136","341265","431652","425163","621534","541362","243165","152346","123645","156342","614532","231546","124365","651234","541326","361254","362415","651243","461253","325416","352614","512643","134256","364512","213654","265413","124356","325164","261345","265314","315624"}

    Returns: 24

  43. {"546213","314256","152346","453621","263145","561342","513246","235461","421653","541623","316524","615324","213456","451326","362451","346512","452361","425136","513462","451263","431625","452613","653214","254613","341256","263451","264351","613524","125364","356412","521436","254163","641325","614325","241365","315642","365214","246153","261453","245631","645321","523416","246351","123654","452316","416325","216345","342165","612354","213546"}

    Returns: 25

  44. {"631245","361452","653214","534621","651342","426531","215463","632541","165342","214536","125463","463512","643152","153624","234615","243561","423651","132645","532461","362451","421635","452316","415326","146253","641532","652314","534261","536124","623451","162453","413652","356214","134562","354261","524136","564132","563142","134625","631542","124635","261543","632514","326415","243516","134256","513246","124356","125346","356124","165432"}

    Returns: 22

  45. {"546321","536412","521364","652341","563412","425136","162543","614325","632541","561234","561324","654321","145326","312465","324165","615324","132465","645321","362514","623415","456321","165432","523614","465123","236154","532461","143652","241563","423516","246513","612534","342516","541623","463125","415623","521463","264513","416235","153264","546123","134652","651423","165324","541362","235416","635421","352164","321564","456231"}

    Returns: 27

  46. {"513426","124536","345261","264315","413265","325416","613524","413256","314625","615243","412365","415326","546231","546312","543126","364215","215436","541623","513246","514263","216453","215634","614523","265134","251436","162453","253614","362451","634125","654312","641235","125463","536421","254631","162534","651342","231654","523461","564213","342651","615324","561423","315264","564132","165324","136254","635421","361524","326154","123456"}

    Returns: 25

  47. {"513246","426531","321645","621345","236415","264153","615342","165342","416325","435126","351642","165423","326154","456123","261345","325416","541632","261453","523461","153462","136245","463125","153426","235146","254136","361524","426153","524361","234561","534126","543216","356214","452163","621534","463521","213456","253614","145326","234651","531642","251436","126543","462135","452631","315426","356241","234516","621435","632154","265431"}

    Returns: 23

  48. {"651324","415623","364521","523461","631542","241356","541632","154326","624315","512346","621534","153624","216543","135246","245163","541623","145623","415632","312546","532461","312645","251634","412536","542136","465321","614352","561423","514326","142653","561243","652413","463152","452613","125643","643521","524361","123654","162453","623451","341526","361245","341625","154263","356412","462135","361524","435261","312456","165234"}

    Returns: 24

  49. {"345162","564231","135624","462315","541623","425136","651234","423561","524163","216345","146532","234615","524136","613245","142365","456123","451623","542631","436125","465321","342165","624513","416253","254361","531624","251463","634152","432156","213564","145623","532416","316425","613254","356421","536124","135426","152364","146253","231546","462531","516243","542613","461352","214653","163542","521643","561234","345621","135264","154263"}

    Returns: 27

  50. {"361425","561243","361245","513264","463512","516342","456213","253614","461523","136452","635241","416253","651423","413652","152346","512643","413526","142365","531426","546123","156423","643215","321546","346125","421563","651324","652413","563412","615324","324156","642153","216345","213645","412536","345216","563241","532146","234156","425136","453126","513462","432516","436152","416235","523146","412365","453621","246531","631254"}

    Returns: 25

  51. {"425631","512436","524316","462315","364215","532641","421635","261534","642351","453612","413526","351624","251643","365421","542163","346125","215463","341562","345126","132564","145236","513264","156243","326514","163254","321564","143652","635124","124356","162453","145632","534612","426135","352614","145362","643152","531624","352164","634512","261543","254136","614235","235641","432561","214536","125643","462531","651324","413265","132456"}

    Returns: 25

  52. {"214536","561324","143625","143265","163425","251346","531426","146532","645231","253641","156234","342615","642531","214635","632154","541236","546132","156432","651342","126435","364152","541263","614253","326451","432165","365124","523641","216435","643152","361245","653214","435261","513642","246513","132456","126354","123546","253416","362415","251643","216453","631245","514326","162534","264315","356214","245361","541623","136524"}

    Returns: 23

  53. {"236514","425163","163254","413526","413256","426153","365241","136524","463521","264153","562143","465312","532641","254316","361524","236154","352146","623451","465132","436152","145236","364251","345621","634251","523164","453621","362541","261543","432156","563421","452613","354612","534612","451236","123645","423516","562341","145326","153264","621345","432651","461352","261354","154236","426531","415623","254361","142536","516423","326451"}

    Returns: 29

  54. {"124653","234516","416235","213465","614235","164235","534216","621453","452613","654312","123546","542316","352146","345216","143562","246135","652314","642513","142356","635142","516432","453216","136425","231645","613452","264351","162345","135642","164532","562341","254163","134562","314652","645132","316542","165423","214356","531246","463251","342156","423156","534612","612354","361425","412563","156423","451362","162543","215643"}

    Returns: 25

  55. {"154623","316452","365214","265413","542136","146523","314256","653142","632514","132645","416253","345162","524361","524631","421635","152463","643152","125634","132456","236154","453612","521436","264351","436125","654312","142365","642351","325416","653421","361245","425316","143625","314265","536412","612345","642135","241563","214365","165234","351462","215643","253614","325164","412536","231546","621543","165243","415326","451236","425613"}

    Returns: 26

  56. {"426315","431652","635142","164523","265413","256341","435612","165234","453216","534612","263514","541263","532164","214365","562341","143526","643521","341256","154236","152643","236145","463512","643251","243651","135462","152436","152463","324165","132654","625134","563142","536142","513246","435126","231456","416523","431526","341265","612543","564321","342156","514326","231546","246315","145326","423651","416325","251463","164235"}

    Returns: 24

  57. {"136542","634125","546132","145632","362451","431265","612453","136524","236145","314265","621435","614235","461253","235461","245361","123564","612354","143526","546123","365421","453126","532146","352461","145263","236415","653412","453216","514632","416235","312546","124635","465231","142635","635421","413526","641532","463215","462513","435261","624513","312645","143256","351426","216345","465312","136425","256314","213645","145326","642513"}

    Returns: 24

  58. {"346125","524136","521364","251643","643215","241365","513624","421356","453216","425163","613245","531264","146253","543126","164253","215643","152643","653421","216435","624315","415263","562134","641523","524361","516324","362154","342165","264351","362541","164235","516423","126435","315624","623541","521463","152364","146352","621435","456312","612345","524163","512346","165342","416325","634521","354126","256413","256134","365412"}

    Returns: 23

  59. {"435612","125346","462351","542163","542631","214365","652413","361542","142356","514362","243651","615432","645132","246135","514326","215436","561324","162453","426315","132546","123456","516342","641523","263415","624315","546123","261345","561234","523146","135642","413562","356142","531642","126345","513264","564213","645123","216543","153462","415326","563214","162354","561432","652314","214536","634215","643215","654312","145623"}

    Returns: 22

  60. {"352641","635124","612345","413562","264513","142536","136425","425631","145362","325146","426135","361245","512643","561432","162453","613452","451362","341526","132546","365124","164523","425361","625143","612534","356214","324156","231564","341652","145263","465321","534216","264153","351624","615234","246531","423651","213456","456231","453612","561243","364512","256413","324561","641532","562431","645213","235614","614523","164352","265143"}

    Returns: 26

  61. {"134526","254136","451623","516243","143562","653412","152364","354612","314562","253614","431625","215643","324561","261534","136452","625341","326145","432615","613254","512364","563412","125346","236514","632415","361245","435612","361254","542316","241653","625134","614352","456213","421563","645213","326154","123645","235614","456312","461253","642135","321465","356142","156342","536241","216435","435621","614325","134256","421536"}

    Returns: 26

  62. {"356241","456132","641523","435126","215436","314652","631254","431256","231654","624153","315426","614532","432615","624351","516243","425361","614325","514236","164235","365124","541263","612543","245163","164253","635214","653412","326514","536241","621543","531246","213564","653421","213645","461352","214536","521364","163524","321465","145263","615342","462351","312564","642513","315246","453162","253461","341562","561423","316425","516432"}

    Returns: 27

  63. {"542631","653142","362145","415632","615423","521436","254631","231645","415623","564213","415362","345261","265341","136452","362451","432165","624315","215463","654132","463521","163254","214563","532164","364251","314256","431652","356421","341526","216543","346125","631254","352641","562314","251346","612345","164253","621453","153264","215634","415236","612534","456213","142635","524361","634125","615342","463215","513264","135642"}

    Returns: 24

  64. {"142356","123465","132564","162345","123456","162453","162354","152463","162543","142563","152346","162534","142536","142365","152643","142635","162435","123564","152436","142653","132546","152364","152634","132645","123546","132465","132456","132654","123654","123645"}

    Returns: 30

  65. {"241356","213465","231564","261345","213456","261453","261354","251463","261543","241563","251346","261534","241536","241365","251643","241635","261435","213564","251436","241653","231546","251364","251634","231645","213546","231465","231456","231654","213654","213645"}

    Returns: 30

  66. {"341256","312465","321564","361245","312456","361452","361254","351462","361542","341562","351246","361524","341526","341265","351642","341625","361425","312564","351426","341652","321546","351264","351624","321645","312546","321465","321456","321654","312654","312645"}

    Returns: 30

  67. {"654312","654132","654231","654213","654123","654321"}

    Returns: 6

  68. {"651423","641253","651342","641325","641235","651432","651243","641352","641523","651234","651324","641532"}

    Returns: 12

  69. {"651234","631254","641352","631425","631245","641532","641253","651432","631524","651342","641325","631542","651324","651243","641523","651423","641235","631452"}

    Returns: 18

  70. {"651432","641235","651324","641253","635421","651423","651234","641325","641352","641532","651243","641523","651342"}

    Returns: 13

  71. {"145326", "154236", "216543" }

    Returns: 3

  72. {"546231", "245631", "531462", "524631", "614235", "415623", "423651", "316254", "432165", "316452", "135426", "643512", "123456", "654321", "543216", "234516" }

    Returns: 12

  73. {"123456", "654312" }

    Returns: 2

  74. {"123456", "124365", "125643", "126534", "214356", "213465", "216543", "215634", "342156", "432165", "562143", "652134", "431256", "341265", "651243", "561234", "563421", "654321", "435621", "346521", "653412", "564312", "345612", "436512" }

    Returns: 1

  75. {"651324", "245163", "246135", "546321", "142536", "314526", "456132", "365241", "125634", "653124", "531624", "542613", "362451", "254631", "164523", "634521", "452613", "641523", "645123", "632514", "324561", "654321", "216453", "136245", "634251", "263154", "645132", "653421", "623514", "265134", "321546", "546231", "142365", "163245", "562341", "562341", "354261", "235614", "236145", "542136", "654321", "613524", "152634", "623154", "451623", "423165", "156324", "652413", "435126", "356241" }

    Returns: 23

  76. {"546231", "245631", "531462", "524631", "614235", "415623", "423651", "316254", "432165", "316452", "135426", "643512", "123456", "124536", "132456", "124356", "123654", "132546", "162345", "123456", "123456", "132465", "132465", "312546", "651234", "542316" }

    Returns: 15

  77. {"142365", "142653", "143256", "143526", "145362", "145623", "146235", "146532", "231456", "234165", "235641", "236514", "261435", "263541", "264153", "265314", "321465", "324156", "325614", "326541", "351462", "352614", "354126", "356241", "412356", "412635", "413265", "413562", "415326", "415632", "416253", "416523", "531426", "532641", "534162", "536214", "561432", "562314", "563241", "564123", "621453", "623514", "624135", "625341", "651423", "652341", "653214", "654132" }

    Returns: 2

  78. {"123456", "654132", "463512", "163524", "451326", "326514", "364521", "164523", "254361", "162543", "165342", "365421", "524361", "164352", "361425", "123456", "123456", "123456" }

    Returns: 12

  79. {"123456", "431256" }

    Returns: 1

  80. {"123456", "123456", "123456" }

    Returns: 1

  81. {"123456", "126534" }

    Returns: 1

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