A test of your logical skills this week….

Four heterosexual men and four heterosexual women are shipwrecked on a desert island.

Eventually each one falls in love with one another, and is loved by one person.   John falls in love with a girl who is, unfortunately, in love with Jim.  Arthur loves a girl who loves the man who loves Ellen.  Mary is loved by the man who is loved by the girl who is loved by Bruce.  Gloria hates Bruce and is hated by the man whom Hazel loves.
Who loves Arthur?

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.

1. Harry Lime says:

Got it in 0.12354225654658 seconds

Depends on the size of his flagpole

1. Kristian says:

he he he

The real problem is: who is going to catch breakfast ?!

4. Mike Hitchcock says:

No-one – they all kill each other in a jealous rage in the first 5 minutes?

1. Berhard says:

I really appreciate this absolute plausible solution…

5. I have a chain of “who loves who” starting and ending with Arthur. Might be other solutions as well, though. Took me just a few minutes.

1. You mean an eight way love cycle?

6. John Loony says:

I think it’s either Adam Werrity or Mike Hancock.

1. CH says:

2. Lazy T says:

werritee hee

7. Bob O'H says:

After half an hour I got 2 graphs & 1 answer.

8. Due to the ending of the world today, could we perhaps have the answer before lunch today, just to be on the safe side?

9. I think I’ve got it – but I am not sure. Tried to match all up.

10. Took me about 10 minutes, needed a pen and paper. That’s not going to be a happy island!

11. About five seconds. I think most of the people who’ve posted above have been looking at this they way you look at those logic puzzles in puzzle books. That’s not how I did it, though tempted at first.

1. There is a way of logically reasoning it out though? I got it in 30 minutes.

2. Anonymous says:

5 seconds?! Just validating each conditions takes longer…

3. Yeah, that’s why I think she is missing something on this one.

4. She could’ve googled for the answer in less than a minute, though that probably shouldn’t count as solving it :p

5. Anonymous says:

I think Catherine must mean she used Google; the answer becomes readily available, second only in the search results to this blog post.

6. Well where is the fun in that!

12. Lazy T says:

Can’t they all just love each other and peace out?
I haven’t got it straightaway and don’t have time to do it now, yipeee a puzzle to ponder in boring meetings hip hip hooray

1. Lazy T says:

The chain fell into place on the second attempt, about five minutes.

13. Maza says:

If it’s J. Arthur it could be all of them

1. nice – “we all love a good J Arthur”

I’ll work it out later with the assistance of a few sheets of paper…

15. Gib says:

10 minutes with a ruby script gives two sets, and arthur loves the same person in both.

16. It was so complicated for Arthur…so he suggested and orgy…everyone agreed…

17. David D says:

Haven’t thought about this yet but the last two weeks puzzles have been really good – back to the standard I’d hoped for. Thank you Richard.

18. Graph Theory from my undergrad helped my reasoning skills in this one I think.

19. Ally says:

I think I got it … but it took me quite a while.

20. I have one answer that, so far as I can see, works, though I’m not sure whether it’s the only possibility. There appear to be some implicit assumptions going on in what is stated though. For instance, is ‘X hates Y’ intended to preclude ‘X loves Y’?

1. Berhard says:

I assume that “X hates Y” should be interpreted as “X does not love Y”, however i assume “X hates Y” actually means “X loves Y, and hates Y because Y does not didn’t respond X’s love but loves Z instead”…..

And by the way love usually precludes logic 😉

2. “however i assume “X hates Y” actually means “X loves Y,” no I do not think this is actually true, I found a solution without it.

3. It’s an assumption, just like the one some have been tempted to make that no love is reciprocal. Is it ever safe to make an assumption in these puzzles? After all, if what was meant was ‘X does not love Y’ then that could simply have been said explicitly. If we’re supposed to assume it, then I’d argue that the puzzle’s not as well-worded as it should be.

4. You think it makes more sense to assume that “X hates Y” is better interpreted as “X loves Y” instead of “X does not love Y”?

lol I hope your real life relationships aren’t reflective of this.

5. “You think it makes more sense to assume that “X hates Y” is better interpreted as “X loves Y””

I never said that; I merely asked whether X hating Y was compatible with X loving Y. Sure it’s unusual, but we’re talking about four heterosexual men and four heterosexual women washed up on a desert island, each one loving and being loved by one other, etc, etc. This isn’t a normal case; it’s a logic puzzle. And, as a logic puzzle, it ought not to rely on us assuming things that aren’t stated in the premises. Otherwise, why not assume, for instance, that no love is reciprocal?

(For what it’s worth, my original answer assumed compatibility, but I think I’ve been able to tweak it so that’s no longer necessary. Nonetheless, it does affect how many solutions there are.)

21. Simon Cowell says:

Reads like the opening sequence from an episode of Glee!

“So here’s what you missed …..”

1. Anonymous says:

Very. Very. Funny.

22. In my solution I assumed if someone hates another person than they definitely do not love them. I thought that was a valid assumption?

23. diavoli says:

I assume nobody loves the person who in turn loves them?

1. Kristian says:

only if you can prove it from the statements

2. No you cannot assume that. :p

3. As there are multiple solutions, you *can* assume that and still come up with a working answer.

4. Yes there are two solutions from what I can see, using this assumption you will only get one of them.

5. Even if that wasn’t the case, there is nothing in the statement to indicate that, that would be a fair assumption.

24. Kristian says:

10 minutes with the help of papers.
Funny puzzle 🙂

Oh and of course, depending on flagpoles, the solution may vary.

25. Ever fallen in love with someone you shouldn’t have fallen in love with?

26. I didn’t trust the wording, so I worked it out.

I have two answers that fit all the requirements!

27. AMWhy says:

There are twoposaible solutions for all the people, but in both Arthur is loved by the same person. About 5mins.

28. song sparrow says:

I think I got it – took 30 min.

29. song sparrow says:

I double checked, and I only see one solution that works, not two.

1. Maarten says:

Same here

30. I think I got it, after five tries I finally got a solution that fit all the requirements. It took me well over an hour.

31. Got 1 solution, it took a pen, a paper and some 10 minutes, by the feel of it (i didn’t time myself).

32. Got it! Half an hour with lots of cut out pieces of paper – thank you Richard!

33. Dan says:

Sounds like something Prolog should be really good at.

34. dani, the geek says:

i only got one solution, and it only took me a couple minutes after i stopped trying to use a standard “logic puzzle” chart and resorted to drawing pictures. spreadsheets make great substitutions for cut-up pieces of paper!

35. And people say that polyamory is a problem.

36. James says:

Took 10min with aid of paper and maybe luck too

37. Gary says:

Jesus, I’ve given up after 10 min’s with paper and pen. X and Y’s, know and unknown number system… etc
Sounds worrying like my life in London rather than a lateral thinking puzzle on a dessert island.
I’m getting a lot of this is unrequited!?

38. Anonymous says:

I solved it by using the names connected with arrows, such as “X->Y” meaning “X loves Y.” Perhaps it would also be useful to point out that all eight names define a ring; e.g., each person loves one and only one other person, each person is loved by one and only one other person, and no person’s love is mutual.

1. These additional restrictions are not true for all possible solutions.

2. Anonymous says:

Oooh, I’ll have to work out the other solution, then. I thought the given conditions implicitly defined those restrictions, but it seems you’re not alone in finding another answer.

39. Amy says:

I can’t even solve this same problem in real life…

40. JimC says:

I think the Smoke Monster loves Arthur.

41. Ed says:

I Love Lucy!

42. Alejandro says:

I’m not sure but I think this was on Gossip Girl.

43. sallybm says:

Well I’ve found one way of doing it. If there’s only one way then that must be it! About 3 minutes, through trial and luck leading to only one, easily-rectifiable, error!

44. astro says:

there is at least one answer, which does not require a graph and is as easy as 22/7.

1. astro says:

wow. after spending a few minutes with an actual diagram, i realized that the “easy” answer is incorrect. there appears, in fact, to be a unique solution.

45. I got the right answer in five minutes, on my first try, and was so surprised that I took the next fifteen to come up with all the wrong answers as well. I agree: there are two answers, unless you add in the requirement that no love be mutual, or that an unspecified ‘girl’ is a different entity than a named girl in the same sentence.

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