# It’s the Friday Puzzle!

60

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 on “It’s the Friday Puzzle!”

1. Simon Taylor says:

Got it straight away. 🙂

• Lord Coe-Cacola says:

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

• Hugh Janus says:

So it must be 9?

2. Roland says:

A magician can never be trusted, so probably 9 3/4 or something 😉

3. Bob O'H says:

Straight away too. I like the simplicity, though.

4. JohnLoony says:

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.

5. Matt Wilkinson says:

1 Min 😛

6. Nigel says:

7. Ale says:

Straight away.

8. Anonymous says:

solved it less then 1 minute

9. Paul Durrant says:

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

10. Ron says:

I got it… Easy peasy x

11. asinrope says:

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

12. Skepdirk says:

Still compatible:

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

13. -M- says:

• -M- says:

(And that is not a spoiler)

• Berhard says:

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

• Martha says:

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

14. 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.

• Skepdirk says:

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.

16. D says:

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

17. John says:

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.

18. Toon says:

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

19. physicalist says:

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

20. Damocles says:

Can we have a mathematical one soon?

• Eddie (@edzeteito) says:

Hear hear!

21. Keith McGregor says:

Got it after reading the final statement.

22. Anne says:

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

I have zero interest in this now.

24. Dharmaruci says:

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

• Martyn says:

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.

• George ("I can not tell a lie, honest Guv") Washington says:

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” ……

25. jumbleguitar says:

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

26. mittfh says:

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?!

27. vignesh says:

5 seconds…

28. Duncan says:

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

29. Scott says:

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

• Chris Emerson says:

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

30. Lazy T says:

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

• Photon Boy says:

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.

• Lord Jelly Coe says:

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

• Wigan FC says:

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

• Nanny Mouse says:

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

• Lazy T says:

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

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.

32. Grammar god says:

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

• Lazy T says:

Exactly!

33. I think I solved it before I read it all, but knowing Richard I’m not too sure 😉

34. Ian says:

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 🙂

35. Paul says:

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

36. edwardv says:

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

37. charm says:

I think I solved it……..;)

38. Nelis says:

Solved exactley in # seconds! 🙂

39. Merari says:

40. Meta Boll**ks says:

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?

41. Raine Wooney says:

Six

42. Paul Murray says: