Can You Find Three Digits for A, B and C Such That ABC in Base-10 Is Equal to CBA in Base-9?

By | August 5, 2019

The only 3-digit answer is \(544_9 = 445_{10}\).

However, there are answers in other bases:

\(211_3 = 112_4\)
\(322_5 = 223_6\)
\(433_7 = 334_8\)
\(544_9 = 445_{10}\)

Are you seeing a pattern here? Does the pattern extended to bases higher than 10?

Does \(655_{10} = 556_{11}\)?

Does \(766_{11} = 667_{12}\)?


Cheating a little bit by using a leading zero, here are some 4-digit answers:

\(1010_2 = 0101_3\)
\(1020_3 = 0201_4\)
\(1030_4 = 0301_5\)
\(1040_5 = 0401_6\)
\(1050_6 = 0501_7\)
\(1060_7 = 0601_8\)
\(1070_8 = 0701_9\)
\(1080_9 = 0801_{10}\)

Are you seeing a pattern here? Does the pattern extended to bases higher than 10?

Does \(1090_{10} = 0901_{11}\)?

Does \(10\rm{A}0_{11} = 0\rm{A}01_{12}\)?

One thought on “Can You Find Three Digits for A, B and C Such That ABC in Base-10 Is Equal to CBA in Base-9?

  1. Chuck Coker

    Here are the answers to “Are you seeing a pattern here? Does the pattern extended to bases higher than 10?”

    Does \(655_{10}=556_{11}\)?
    No. \(655_{10} \ne 666_{10}\)

    Does \(766_{11}=667_{12}\)?
    No. \(919_{10} \ne 943_{10}\)

    Does \(1090_{10} = 0901_{11}\)?
    Yes. \(1090_{10} = 1090_{10}\)

    Does \(10\rm{A}0_{11} = 0\rm{A}01_{12}\)?
    Yes. \(1441_{10} = 1441_{10}\)

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