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

  2. 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

  3. 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.

  4. 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. 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. 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.

    3. “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.)

  5. 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!

  6. 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!?

  7. 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. 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.

  8. 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!

    1. 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.

  9. 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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