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Fill in the blanks with only words - no digits allowed.

It is false to say that the letter 't' appears ________ times in this sentence.
It is _____ to say that the letter 'f' appears _____ times in this paragraph.
It is ______ to say that the letter 't' appears forty-six times in this paragraph.
It is true to say that the letter 'e' appears ______ times in this sentence.

(Note: All statements only refer to the four lines in the yellow box.)

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    $\begingroup$ Does the "paragraph" start with "Fill..." or is it the four sentences? $\endgroup$
    – Paul Evans
    Commented Mar 12, 2016 at 23:14
  • $\begingroup$ @PaulEvans the 'paragraph' only refers to the 4 main sentences $\endgroup$
    – Ben
    Commented Mar 13, 2016 at 10:47
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    $\begingroup$ Is counting considered to be in-scope for the calculation tag you're using? The tag explanation talks about calculations like multiplication and additions, and I don't see any such operations beyond counting. $\endgroup$
    – Lawrence
    Commented Mar 14, 2016 at 15:18
  • $\begingroup$ @Lawrence Is counting not addition?? $\endgroup$
    – Ben
    Commented Mar 14, 2016 at 15:26
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    $\begingroup$ @Ben, counting is not addition. Counting is indexing. The fact that you happen to be indexing using integers increasing from 0 at a rate of 1 per item does not make it calculation. $\endgroup$
    – Ian MacDonald
    Commented Mar 14, 2016 at 16:58

5 Answers 5

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One solution is:

It is false to say that the letter 't' appears two times in this sentence.
It is true to say that the letter 'f' appears four times in this paragraph.
It is true to say that the letter 't' appears forty-six times in this paragraph.
It is true to say that the letter 'e' appears twelve times in this sentence.

Of course:

The two in the first sentence can be replaced with any number that has one 't' (and no 'f') in it except twelve.
The last sentence can't change - it's the only solution.
I'm sure there's waggle room in the two middle sentences which then means the first sentence might have to be revisited.

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  • $\begingroup$ nice - I had a slightly different solution in mind re: the waggle room in the middle and slight change in the first... But this works! $\endgroup$
    – Ben
    Commented Mar 13, 2016 at 10:51
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A somewhat less rational solution than the one provided by Paul Evans:

It is false to say that the letter 't' appears pi times in this sentence.
It is false to say that the letter 'f' appears pi times in this paragraph.
It is possible to say that the letter 't' appears forty-six times in this paragraph.
It is true to say that the letter 'e' appears at least two times in this sentence.

As Paul Evans points out in his answer, there are many possible solutions. I just decided on an irrational one.

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  • $\begingroup$ I suppose it's not fair to take advantage of the fact that it isn't explicitly stated that the sentences have to be true. $\endgroup$
    – Hugh Meyers
    Commented Mar 13, 2016 at 10:30
  • $\begingroup$ @HughMeyers - Every sentence in this answer is technically true. They're just not very specific. $\endgroup$
    – Darrel Hoffman
    Commented Mar 13, 2016 at 16:26
  • $\begingroup$ @DarrelHoffman I realized that. I meant that another avenue to being irrational would be to fill the blanks with random words since there is no explicit requirement for the sentences to be true. Of course it wouldn't be entirely fair since truth is a pretty standard implicit requirement. $\endgroup$
    – Hugh Meyers
    Commented Mar 13, 2016 at 16:33
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    $\begingroup$ Can't resist: It would be $\underline{\sf ungrammatical}$ to say that the letter 'f' appears $\underline{\sf one}$ times in this paragraph. $\endgroup$
    – humn
    Commented Mar 14, 2016 at 9:38
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Wouldn't this be the simplest solution?

It is false to say that the letter 't' appears zero times in this sentence.
It is false to say that the letter 'f' appears zero times in this paragraph.
It is false to say that the letter 't' appears forty-six times in this paragraph.
It is true to say that the letter 'e' appears twelve times in this sentence.

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  • $\begingroup$ yep (...scratching head) I suppose it is :-p $\endgroup$
    – Ben
    Commented Mar 15, 2016 at 17:23
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I decided to put the extra challenge of fitting many words into the blanks.

It is false to say that the letter 't' appears to be written more than thirty thousand times in this sentence.
It is incorrect but not impossible to say that the letter 'f' appears to be formatted using a different font four hundred fifty five times in this paragraph.
It is inconsequential whether or not it is easy to say that the letter 't' appears forty-six times in this paragraph.
It is true to say that the letter 'e' appears less than twenty two times but greater than three times in this sentence.

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  • $\begingroup$ How can the letter 'f' be formatted differently 455 times if it only appears 11 times!!!? Methinks 'tis surely impossible... :-) good job though! $\endgroup$
    – Ben
    Commented Mar 14, 2016 at 15:29
  • $\begingroup$ The statement is incorrect (as noted). Because the statement has been made, it is clearly not impossible to say. It is certainly possible to say untrue statements. $\endgroup$
    – Ian MacDonald
    Commented Mar 14, 2016 at 15:34
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As others have done, I decided to go for a roundabout answer. Let's start of with whether or not we know an answer.

It is false to say that the letter 't' appears an indeterminate number of times in this sentence.

So it seems we know something about the answer. What else do we know about the answer?

It is quite silly to say that the letter 'f' appears burrito times in this paragraph.

Well, that rules out that type of answer. How about a true (and logical) one?

It is entirely truthful, to say little of other matters, particularly so of the town’s terrible titans of typography, who typically rant tumultuously about the excess of the letter ‘t’ in run-on sentences such as the present example (for which I have to give them credit where it is quite due, for I myself seem to have violated the unspoken rule), to say the letter t appears forty-six times in this paragraph.

...Can you give a shorter answer, please? That was obnoxious.

It is true to say that the letter 'e' appears at predetermined times in this sentence.

I guess I will give up on getting a good answer, then.

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  • $\begingroup$ The word "paragraph" in the puzzle is intended to reference all four lines together, making your statement on the third line actually false. $\endgroup$
    – Ian MacDonald
    Commented Mar 14, 2016 at 18:34
  • $\begingroup$ Probably so, but this way was a dialogue, which made them other paragraphs, I guess? Oh well, it was fun anyway! $\endgroup$
    – charfellow
    Commented Mar 14, 2016 at 18:57

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