perplexus.info :: Numbers : Who's on the 4th base?

Who's on the 4th base? (Posted on 2019-05-28)

21 is a palindrome in 4 distinct bases (bases: 2,4,6,20 ==> 10101,111,33,11,)

Find the smallest 3-digit number N such that both this number and its reversal are palindromes in at least 4 distinct bases.

Both number 1 and numbers higher than N do not qualify as bases.
Base 10 is in.

No Solution Yet Submitted by Ady TZIDON

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computer solution and extension (2)

Comment 3 of 3 |

There are 208 such reversal pairs. Some of the numbers are palindromic in base 10 and others are not. As a result, the number of such numbers, altogether, is 374 as 42 are palindromic and do not count for two different numbers.

So more than 1/3 png to ico of the 3-digit numbers satisfy the conditions.

An extreme example is 468 and 864; the former has 10 palindromic representations and the latter has 12.

Posted by faithbaker on 2020-08-14 03:56:12

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