Cubes with same digits

 
 
The digits of
5^3 \; = \; 125
can be permuted to form
8^3 \; = \; 512
 

cube whose digits can be permuted to produce two other cubes :

345^3 \; = \; 41063625
384^3 \; = \; 56623104
405^3 \; = \; 66430125
 

1001^3 \; = \; 1003003001
1010^3 \; = \; 1030301000
1100^3 \; = \; 1331000000
 

1028^3 \; = \; 1086373952
1112^3 \; = \; 1375036928
1721^3 \; = \; 5097328361
 

1088^3 \; = \; 1287913472
1238^3 \; = \; 1897413272
1571^3 \; = \; 3877292411
 

1273^3 \; = \; 2062933417
1447^3 \; = \; 3029741623
2101^3 \; = \; 9274236301
 

1532^3 \; = \; 3595640768
1889^3 \; = \; 6740558369
1919^3 \; = \; 7066834559
 

1733^3 \; = \; 5204699837
1895^3 \; = \; 6804992375
2033^3 \; = \; 8402569937

 

and three other cubes :

1002^3 \; = \; 1006012008
1020^3 \; = \; 1061208000
2001^3 \; = \; 8012006001
2010^3 \; = \; 8120601000

 
 
Paul found:

10001^3 \; = \; 1000300030001
10010^3 \; = \; 1003003001000
10100^3 \; = \; 1030301000000
11000^3 \; = \; 1331000000000
 

10002^3 \; = \; 1000600120008
10020^3 \; = \; 1006012008000
10200^3 \; = \; 1061208000000
20001^3 \; = \; 8001200060001
20010^3 \; = \; 8012006001000
20100^3 \; = \; 8120601000000
 

10003^3 \; = \; 1000900270027
10030^3 \; = \; 1009027027000
10300^3 \; = \; 1092727000000
 

10004^3 \; = \; 1001200480064
10040^3 \; = \; 1012048064000
10400^3 \; = \; 1124864000000
 

10017^3 \; = \; 1005108674913
14589^3 \; = \; 3105107018469
17001^3 \; = \; 4913867051001
 

10018^3 \; = \; 1005409725832
17650^3 \; = \; 5498372125000
18001^3 \; = \; 5832972054001
20419^3 \; = \; 8513407220059
 

10047^3 \; = \; 1014166373823
13896^3 \; = \; 2683301147136
19146^3 \; = \; 7018336124136
 

10059^3 \; = \; 1017804635379
12117^3 \; = \; 1779038405613
17883^3 \; = \; 5719013604387
 

10093^3 \; = \; 1028160274357
10267^3 \; = \; 1082257704163
13027^3 \; = \; 2210717450683

 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

2 Responses to Cubes with same digits

  1. Paul says:

    Here are a few 5 digit ones, notice how some n and n^3 each contain the same digits.
    I have a feeling there will be a lot of 5 digit variants.

    {10001,^3 -> ,10001,^3, = ,1000300030001}
    {10001,^3 -> ,10010,^3, = ,1003003001000}
    {10001,^3 -> ,10100,^3, = ,1030301000000}
    {10001,^3 -> ,11000,^3, = ,1331000000000}

    {10002,^3 -> ,10002,^3, = ,1000600120008}
    {10002,^3 -> ,10020,^3, = ,1006012008000}
    {10002,^3 -> ,10200,^3, = ,1061208000000}
    {10002,^3 -> ,20001,^3, = ,8001200060001}
    {10002,^3 -> ,20010,^3, = ,8012006001000}
    {10002,^3 -> ,20100,^3, = ,8120601000000}

    {10003,^3 -> ,10003,^3, = ,1000900270027}
    {10003,^3 -> ,10030,^3, = ,1009027027000}
    {10003,^3 -> ,10300,^3, = ,1092727000000}

    {10004,^3 -> ,10004,^3, = ,1001200480064}
    {10004,^3 -> ,10040,^3, = ,1012048064000}
    {10004,^3 -> ,10400,^3, = ,1124864000000}

    {10010,^3 -> ,10001,^3, = ,1000300030001}
    {10010,^3 -> ,10010,^3, = ,1003003001000}
    {10010,^3 -> ,10100,^3, = ,1030301000000}
    {10010,^3 -> ,11000,^3, = ,1331000000000}

    {10017,^3 -> ,10017,^3, = ,1005108674913}
    {10017,^3 -> ,14589,^3, = ,3105107018469}
    {10017,^3 -> ,17001,^3, = ,4913867051001}

    {10018,^3 -> ,10018,^3, = ,1005409725832}
    {10018,^3 -> ,17650,^3, = ,5498372125000}
    {10018,^3 -> ,18001,^3, = ,5832972054001}
    {10018,^3 -> ,20419,^3, = ,8513407220059}

    {10020,^3 -> ,10002,^3, = ,1000600120008}
    {10020,^3 -> ,10020,^3, = ,1006012008000}
    {10020,^3 -> ,10200,^3, = ,1061208000000}
    {10020,^3 -> ,20001,^3, = ,8001200060001}
    {10020,^3 -> ,20010,^3, = ,8012006001000}
    {10020,^3 -> ,20100,^3, = ,8120601000000}

    {10030,^3 -> ,10003,^3, = ,1000900270027}
    {10030,^3 -> ,10030,^3, = ,1009027027000}
    {10030,^3 -> ,10300,^3, = ,1092727000000}

    {10040,^3 -> ,10004,^3, = ,1001200480064}
    {10040,^3 -> ,10040,^3, = ,1012048064000}
    {10040,^3 -> ,10400,^3, = ,1124864000000}

    {10047,^3 -> ,10047,^3, = ,1014166373823}
    {10047,^3 -> ,13896,^3, = ,2683301147136}
    {10047,^3 -> ,19146,^3, = ,7018336124136}

    {10059,^3 -> ,10059,^3, = ,1017804635379}
    {10059,^3 -> ,12117,^3, = ,1779038405613}
    {10059,^3 -> ,17883,^3, = ,5719013604387}

    {10093,^3 -> ,10093,^3, = ,1028160274357}
    {10093,^3 -> ,10267,^3, = ,1082257704163}
    {10093,^3 -> ,13027,^3, = ,2210717450683}

    {10100,^3 -> ,10001,^3, = ,1000300030001}
    {10100,^3 -> ,10010,^3, = ,1003003001000}
    {10100,^3 -> ,10100,^3, = ,1030301000000}
    {10100,^3 -> ,11000,^3, = ,1331000000000}

    Paul.

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