Base 12: Final Numbers: Fixed Points

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789AB

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany calculation that has no results

Digits # Cycles
(excluding fixed)
(excluding zero)
# Fixed Points
(cycle length 1)
(excluding zero)
Fixed Points
(excluding zero)
(bold = exactly 1 fixed point [excluding zero], no other cycles)
10 cycles0 fixed pts-
21 cycle 0 fixed pts-
30 cycles1 fixed pt 5B6
42 cycles0 fixed pts-
51 cycle 1 fixed pt 83B74
61 cycle 1 fixed pt 65BB56
71 cycle 1 fixed pt 962B853
81 cycle 2 fixed ptsA850A632, 873BB744
93 cycles1 fixed pt 665BBB556
103 cycles1 fixed pt 8843BB7734
112 cycles2 fixed ptsA8641B97532, 8773BBB7444
125 cycles2 fixed ptsB97530A86421, 6665BBBB5556
133 cycles1 fixed pt 88743BBB77434
148 cycles4 fixed pts986532BB886533, 996632BB885523, BB97530A864201, 87773BBBB74444
152 cycles2 fixed pts888443BBB777334, 66665BBBBB55556
1618 cycles2 fixed ptsBBB97530A8642001, 887743BBBB774434
172 cycles2 fixed ptsBA986530BA8653211, 877773BBBBB744444
1836 cycles5 fixed ptsA98755310AA8664322, A9866431BB98755322, BBBB97530A86420001, 8887443BBBB7774334, 666665BBBBBB555556
192 cycles2 fixed ptsBBA986530BA86532101, 8877743BBBBB7744434
2067 cycles4 fixed ptsA98765421BB997654322, BBBBB97530A864200001, 8777773BBBBBB7444444, 88884443BBBB77773334
213 cycles6 fixed ptsBBBA986530BA865321001, 988655332BBB888665333, 998665332BBB888655323, 999666332BBB888555223, 88877443BBBBB77744334, 6666665BBBBBBB5555556
22117 cycles4 fixed ptsAA88664421BB9977553312, B9977553310AA886644221, BBBBBB97530A8642000001, 88777743BBBBBB77444434
232 cycles4 fixed ptsBA987654320BA9876543211, BBBBA986530BA8653210001, 87777773BBBBBBB74444444, 888874443BBBBB777743334
24191 cycles5 fixed ptsA9876644321BB99877554322, BB9977553310AA8866442201, BBBBBBB97530A86420000001, 888777443BBBBBB777444334, 66666665BBBBBBBB55555556
253 cycles5 fixed ptsA9986664331BBB98875553222, BBA987654320BA98765432101, BBBBBA986530BA86532100001, 887777743BBBBBBB774444434, 8888844443BBBBB7777733334
26303 cycles4 fixed ptsBBB9977553310AA88664422001, BBBBBBBB97530A864200000001, 877777773BBBBBBBB744444444, 8888774443BBBBBB7777443334
276 cycles5 fixed ptsA99876654321BBB998765543222, BBBA987654320BA987654321001, BBBBBBA986530BA865321000001, 8887777443BBBBBBB7774444334, 666666665BBBBBBBBB555555556
28459 cycles10 fixed ptsBAA9886654320BBA987655332111, A9987755533110AAA88666443222, BBBB9977553310AA886644220001, 998866553332BBBB888866553323, 988865553332BBBB888866653333, 999966663332BBBB888855552223, 999866653332BBBB888865553223, BBBBBBBBB97530A8642000000001, 8877777743BBBBBBBB7744444434, 88888744443BBBBBB77777433334
2913 cycles6 fixed ptsAA98866644321BBB9987755533212, A998776554221BBB9997665443222, BBBBA987654320BA9876543210001, BBBBBBBA986530BA8653210000001, 8777777773BBBBBBBBB7444444444, 88887774443BBBBBBB77774443334
30675 cycles6 fixed ptsBBAA9886654320BBA9876553321101, BBBBB9977553310AA8866442200001, BBBBBBBBBB97530A86420000000001, 888888444443BBBBBB777777333334, 88877777443BBBBBBBB77744444334, 6666666665BBBBBBBBBB5555555556
3128 cycles5 fixed ptsAA988766544221BBB99977655433212, BBBBBA987654320BA98765432100001, BBBBBBBBA986530BA86532100000001, 88777777743BBBBBBBBB77444444434, 888887744443BBBBBBB777774433334
32967 cycles8 fixed ptsB999777555333110AAA8886664442221, A9998666643331BBBB98887555532222, BAA998866553310BBAA8866553322111, BBBAA9886654320BBA98765533211001, BBBBBB9977553310AA88664422000001, BBBBBBBBBBB97530A864200000000001, 87777777773BBBBBBBBBB74444444444, 888877774443BBBBBBBB777744443334
3354 cycles8 fixed ptsAAA888666444221BBB999777555333112, BA99877655433210BAA98876654432211, A99877665443221BBB999877655443222, BBBBBBA987654320BA987654321000001, BBBBBBBBBA986530BA865321000000001, 888777777443BBBBBBBBB777444444334, 8888887444443BBBBBBB7777774333334, 66666666665BBBBBBBBBBB55555555556