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Programatically it is easy to construct all 520 sentences and count those that are true.

This Python program runs in 30ms.

Solution:28 of the sentences are true.This is not a difficult enigma conceptually but I am getting 29 true statements : h has no true statement;i,r,s and w each has two correct statements and the rest of the alphabet each has one correct statement for a total of 29 correct statements. Please point out where I have gone astray.

There are no true sentences for the letter “o”.

This brings your total down to 28.

Here’s an analytical solution.

Counting the letters in the partial sentence: “The number of _’s in this sentence is _”. We get the following categories:

5 = e

4 = n, s

3 = i, t

2 = h

1 = b, c, f, m, o, r, u

0 = a, d, g, j, k, l, p, q, v, w, x, y, z

If we now consider completing the sentence by adding a letter (so the count will always be at least 1) and a number as a word:

For the number “one” the sentence can only be true for letters in category 0 that don’t appear in “one” (which is all of them): a, d, g, j, k, l, p, q, v, w, x, y, z (13 letters).

For “two” the sentence can be true for letters in category 1 that don’t appear in “two”: b, c, f, m, r, u (6 letters), or letters in category 0 that appear in “two” once: w (1 letter).

For “three” we need letters in category 2 but not in “three”: (0 letters), or letters in category 1 that appear in “three” once: r (1 letter), or letters in category 0 that appear in “three” twice: (0 letters).

For “four” we need letters in category 3 but not in “four”: i, t (2 letters) or letters in category 2 that appear in “four” once: (0 letters).

For “five” we need letters in category 4 but not in “five”: n, s (2 letters) or letters in category 3 that appear in “five” once: i (1 letter).

For “six” we need letters in category 5 but not in “six”: e (1 letter) or letters in category 4 that appear in “six” once: s (1 letter).

For “seven” there is no category 6 so we only need to look for letters in category 5 that appear in “seven” once: (0 letters), or letters in category 4 that appear in “seven” twice (0 letters).

Higher numbers don’t add enough letters to allow us to look in category 5 or less.

So the grand total is that 28 of the sentences are true.