Articles from January, 2010

Counting Binary and Hexadecimal Palindromes

How many nonzero, n-digit, decimal number palindromes are there? These two formulas give the answer:

  • When n is even: 9·10n/2-1
  • When n is odd: 9·10(n+1)/2-1

How many nonzero, decimal number palindromes are there, consisting of n-digits or less? These two formulas give the answer:

  • When n is even: 2(10n/2 – 1)
  • When n is odd: 11·10(n-1)/2 – 2

So for example, there are 900 5-digit decimal palindromes, 9,000 8-digit decimal palindromes, 1,098 decimal palindromes of 5 digits or less, and 19,998 decimal palindromes of 8 digits or less.

In this article, I will derive similar formulas to count binary and hexadecimal number palindromes.

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