A palindrome is a number that reads the same forward and backward. What is the smallest 5-digit palindrome in base 2 that can be expressed as a 2-digit palindrome in a different base? Give your response in base 2.

A 2 digit palindrome in any base would have to be x x as in 11 22 33 44 55 66 ....99

which of these is a palindrome in base 2?

(the only 5 digit base two numbers are 16-31_{10 }palindromes include 17 21 27 31)

27 in base 2 = 11011

27 = 33_{8}

Guest is certainly correct.

Another answer is 11_{base 26}

So

The smallest base 2 five digit palindrone is 10001_{2} = 17_{10}

_{\(10001_2=17_{10}=33_8=11_{26}\)}