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.

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Got it straight away. :)

Of necessity (they contradict one another) at most one. And therefore …..

So it must be 9?

A magician can never be trusted, so probably 9 3/4 or something ;-)

Straight away too. I like the simplicity, though.

About 20 seconds… I’m not sure what the “twist” might be, except that the twist is probably the fact that there isn’t a twist.

1 Min :P

Oooh, my head!

Straight away.

solved it less then 1 minute

A remarkably easy one this week, I think. I suppose I’ll find out if I am right about its difficulty on Monday!

I got it… Easy peasy x

I think I have it, although I am second guessing myself now!

Still compatible:

11) It took you longer than 20 seconds to figure it out.

There are 2 possible answers!

(And that is not a spoiler)

thanks making me search for the second solution…

and i actually don’t consider your comment as a spoiler…

It should have gone ‘Exactly ten…’, ‘Exactly nine…’ etc.

The only twist I can think of is if “these statements” doesn’t only refer to numbered statements, but that would be a cheat, imo.

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.

Hmm. I’m pretty sure that wording has been changed since I posted, Skepdirk.

Seems straight forward, so think I solved it in less than 20 seconds.

It was so easy, I’m doubting I have the right answer. :|

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.

Took me about 10 seconds. It looks hard at first, but it isn’t.

Easy (unless I’m missing something). Got it before I finished reading.

Can we have a mathematical one soon?

Hear hear!

Got it after reading the final statement.

Yay, my first easy one!! Got it straight away!

I have zero interest in this now.

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

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.

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” ……

Interested to see which one of my two answers is deemed correct, and why the other one isn’t.

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?!

5 seconds…

I got it before I finished reading all the statements – unless there’s some huge twist I completely missed!

I got it in 5 seconds, but there are two answers.

Got it straight away, but I can only see one answer…

I have two answers depending on exactly how I interpret ‘exactly’

I now have several infinite series of solutions, including a pretty fractal one.

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

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

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.

I have up to 153 answers depending on how truly I interpret the word “true”

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.

I have two answers depending on the referent for each use of the word “these”

Exactly!

I think I solved it before I read it all, but knowing Richard I’m not too sure ;)

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 :)

I got it right away. I think. Then I had to read through it to be sure I wasn’t missing anything.

It seems there are two equally valid answers unless the question is reworded or a statement is added.

I think I solved it……..;)

Solved exactley in # seconds! :)

about 20 seconds

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?

Six

There are two answers.

This seemed too easy and I’m usually hopeless about true/false puzzles.