perplexus.info :: Just Math : Simultaneous Base Baffle

Simultaneous Base Baffle (Posted on 2014-09-17)

Determine the smallest value of a positive integer N such that N is a palindrome in both base 3 and base 10. What is the next smallest value of N having this property?

*** N must have more than one digit in any base. So, trivial solutions like (4)_{base 10} or, (8)_{base 10} are not permissible.

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

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re: solution

| Comment 2 of 6 |

(In reply to solution by Ady TZIDON)

111 in base 3 is 110101, while 111111 in base 3 is 364.

The latter is (3^6-1) / 2, as 2 is the highest base-3 digit so that 222222 is 3^6 - 1.

Posted by Charlie on 2014-09-17 15:36:48

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