Here are 10 numbered statements.  How many of them are true?

1) Exactly one of these statements is true.

2) Exactly two of these statements are true.

3) Exactly three of these statements are true.

4) Exactly four of these statements are true.

5) Exactly five of these statements are true.

6) Exactly six of these statements are true.

7) Exactly seven of these statements are true.

8) Exactly eight of these statements are true.

9) Exactly nine of these statements are true.

10) Exactly ten of these statements are true.

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

60 comments

    1. thanks making me search for the second solution…
      and i actually don’t consider your comment as a spoiler…

    1. Also, the question says “How many of *them* are true”, so I think we can be pretty sure that it’s indeed only about the numbered statements.

  1. Think I got it in about 30 sec then about a minute of logical thinking to check and test a few alternatives in my head.

  2. ans seems trivial. i got ans immediately.

    harder promble would be:
    1) Exactly one of these statements is true (but not this one)
    2) Exactly two of these statements are true (but not including this one)
    etc

    1. I thought it might make it a bit less straight-forward if it had some variations on ‘exactly’, like ‘up to’, ‘at least’, ‘approximately’ (to piss off the pedants) and so on.

    2. or
      “None of these statements are true excluding this one”
      “None of these statements are true including this one”
      “This statement is neither true nor false”
      “This statement is both true and false”
      “This statement is true only to the extent it is self-referential”
      “This statement is only true to the extent it is not self-referential” ……

  3. After getting to about the third numbered statement, I’d spotted the pattern, and a few more seconds of thinking revealed one answer…

    …but surely it can’t be *that* easy, can it?! Surely there’s got to be a twist if *I* can solve it in under ten seconds?!

    1. You can have 153 different solutions if you assign 153 different meanings to the word “exactly”. No interpretation of the word “exactly” is required. Its meaning is quite clear.

    2. Damn you. I have 152 answers (depending on how accurately I interpret the word “accurately”).

    3. The answer is ten, depending on interpreting the words one, two, three, four, five, six, seven, eight, and nine as being the word “ten”.

  4. Took me as long as it took to read it, plus a very long time after wondering if my answer was just to simple or the question too easy.
    This seems to be a meta/self referential puzzle like last week. Hope that does not constitute a spoiler.

  5. I like that one, thanks: sort of clever and obvious at the same time. Got the answer straight away, but that doesn’t mean I’ve not been tripped up by something I might’ve read awry. Thanks for another good one and have an excellent weekend 🙂

  6. To paraphrase President Bill Clinton “it depends on what you mean by true”
    PS Isn’t anyone going to moan about the spoiler at the very beginning of this thread?

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