# 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. $$1441_{10} = 1441_{10}$$