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Old 2020-02-11, 03:12   #1
sweety439
 
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Nov 2016
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Default Find Kaprekar's constants and cycles of the Kaprekar mapping of 9-digit to 12-digit numbe in base 12

Can someone find all the 9-digit to 12-digit cycles of the Kaprekar mapping in base 12? I cannot find them, since the range is too large, can someone help me? I only have data for base 10 and base 16 to 20 digits, but no base 12, and I myself searched base 12 to 8 digits and find the cycles:

Code:
Digit length	Cycles	Cycle lengths	Number of cycles
1	{0}	1	1
2	{00}, {0E, X1, 83, 47, 29, 65}	1, 6	2
3	{000}, {5E6}	1, 1	2
4	{0000}, {3EE8, 8284, 6376}, {4198, 8374, 5287, 6196, 7EE4, 7375}	1, 3, 6	3
5	{00000}, {64E66, 6EEE5}, {83E74}	1, 2, 1	3
6	{000000}, {420X98, X73742, 842874, 642876, 62EE86, 951963, 860X54, X40X72, X82832, 864654}, {65EE56}	1, X, 1	3
7	{0000000}, {841E974, X53E762, 971E943, X64E652, 960EX53, E73E741, X82E832, 984E633, 863E754}, {962E853}	1, 9, 1	3
8	{00000000}, {4210XX98, X9737422, 87428744, 64328876, 652EE866, 961EE953, X8428732, 86528654, 6410XX76, X92EE822, 9980X323, X7646542, 8320X984, X7537642, 8430X874, X5428762, 8630X854, X540X762, X830X832, X8546632, 8520X964, X740X742, X8328832, 86546654}, {873EE744}, {X850X632}	1, 20, 1, 1	4
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