As you know, a palindrome is a word, phrase or sentence for which the order of the letters is the same when reversed: "A man, a plan, a canal: Panama!". We can always associate with any palindrome the number of letters *L* . We don't include punctuation, so for our example we have *L* = 21.

It's difficult to construct a palindrome, because the first letter must match the last letter, the second letter must match the second last letter, and so on. However, if *L* is odd, we catch a bit of a break, since the middle letter doesn't have to be matched. Does this mean it's easier to construct a palindrome of odd length? If so, there should be more palindromes of this type.

This can be tested. I've done it several times, and each time I counted significantly more palindromes of odd than even length.

For this example I used a list of 460 palindromes from a website __Neil/Fred's Gigantic List of Palindromes__ (notice is given that this website is no longer maintained).

I copied the palindromes, and after processing them I found 340/460 of the palindromes were of odd length (about 74%, a test against a null hypothesis of 50% yields P-value = very tiny number). Here are two frequency plots of the palindrome lengths. The first plot is not very illuminating, so I created a second frequency plot using only palindromes of length 50 or less. In between* L* = 4 and *L* = 45, the frequencies increase then decrease as we move from even to odd then to even values of *L*. So I guess it's true.

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