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.
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October 21, 2011 at 7:32 am |
Got it in 0.12354225654658 seconds
October 21, 2011 at 7:35 am |
Depends on the size of his flagpole
October 21, 2011 at 1:41 pm
he he he
October 21, 2011 at 7:42 am |
The real problem is: who is going to catch breakfast ?!
October 21, 2011 at 7:42 am |
No-one – they all kill each other in a jealous rage in the first 5 minutes?
October 21, 2011 at 3:56 pm
I really appreciate this absolute plausible solution…
October 21, 2011 at 7:48 am |
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.
October 21, 2011 at 4:11 pm
You mean an eight way love cycle?
October 21, 2011 at 7:54 am |
I think it’s either Adam Werrity or Mike Hancock.
October 21, 2011 at 7:57 am
Made me literally lol.
October 21, 2011 at 10:00 am
werritee hee
October 21, 2011 at 7:56 am |
After half an hour I got 2 graphs & 1 answer.
October 21, 2011 at 7:58 am |
Due to the ending of the world today, could we perhaps have the answer before lunch today, just to be on the safe side?
October 21, 2011 at 8:26 am
GMT please.
October 21, 2011 at 8:16 am |
I think I’ve got it – but I am not sure. Tried to match all up.
October 21, 2011 at 8:32 am |
Took me about 10 minutes, needed a pen and paper. That’s not going to be a happy island!
October 21, 2011 at 9:00 am |
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.
October 21, 2011 at 11:13 am
There is a way of logically reasoning it out though? I got it in 30 minutes.
October 21, 2011 at 1:00 pm
5 seconds?! Just validating each conditions takes longer…
October 21, 2011 at 4:02 pm
Yeah, that’s why I think she is missing something on this one.
October 21, 2011 at 4:32 pm
She could’ve googled for the answer in less than a minute, though that probably shouldn’t count as solving it :p
October 21, 2011 at 8:46 pm
I think Catherine must mean she used Google; the answer becomes readily available, second only in the search results to this blog post.
October 21, 2011 at 10:44 pm
Well where is the fun in that!
October 21, 2011 at 9:58 am |
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
October 23, 2011 at 12:29 pm
The chain fell into place on the second attempt, about five minutes.
October 21, 2011 at 10:04 am |
If it’s J. Arthur it could be all of them
October 21, 2011 at 2:39 pm
nice – “we all love a good J Arthur”
October 21, 2011 at 10:21 am |
My head hurts!
I’ll work it out later with the assistance of a few sheets of paper…
October 21, 2011 at 10:37 am |
10 minutes with a ruby script gives two sets, and arthur loves the same person in both.
October 21, 2011 at 10:57 am |
It was so complicated for Arthur…so he suggested and orgy…everyone agreed…
October 21, 2011 at 11:11 am |
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.
October 21, 2011 at 11:14 am |
Graph Theory from my undergrad helped my reasoning skills in this one I think.
October 21, 2011 at 11:17 am |
I think I got it … but it took me quite a while.
October 21, 2011 at 12:08 pm |
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’?
October 21, 2011 at 3:53 pm
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
October 21, 2011 at 4:05 pm
“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.
October 22, 2011 at 11:40 am
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.
October 22, 2011 at 11:46 pm
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.
October 23, 2011 at 12:30 am
“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.)
October 21, 2011 at 12:15 pm |
Reads like the opening sequence from an episode of Glee!
“So here’s what you missed …..”
October 23, 2011 at 11:55 am
Very. Very. Funny.
October 21, 2011 at 12:53 pm |
In my solution I assumed if someone hates another person than they definitely do not love them. I thought that was a valid assumption?
October 21, 2011 at 1:09 pm |
I assume nobody loves the person who in turn loves them?
October 21, 2011 at 1:43 pm
only if you can prove it from the statements
October 21, 2011 at 4:03 pm
No you cannot assume that. :p
October 21, 2011 at 4:30 pm
As there are multiple solutions, you *can* assume that and still come up with a working answer.
October 21, 2011 at 10:45 pm
Yes there are two solutions from what I can see, using this assumption you will only get one of them.
October 21, 2011 at 10:46 pm
Even if that wasn’t the case, there is nothing in the statement to indicate that, that would be a fair assumption.
October 21, 2011 at 1:46 pm |
10 minutes with the help of papers.
Funny puzzle
Oh and of course, depending on flagpoles, the solution may vary.
October 21, 2011 at 2:10 pm |
Ever fallen in love with someone you shouldn’t have fallen in love with?
October 21, 2011 at 2:15 pm |
I didn’t trust the wording, so I worked it out.
I have two answers that fit all the requirements!
October 21, 2011 at 2:46 pm |
There are twoposaible solutions for all the people, but in both Arthur is loved by the same person. About 5mins.
October 21, 2011 at 2:53 pm |
I think I got it – took 30 min.
October 21, 2011 at 2:58 pm |
I double checked, and I only see one solution that works, not two.
October 23, 2011 at 3:45 pm
Same here
October 21, 2011 at 3:28 pm |
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.
October 21, 2011 at 3:42 pm |
Got 1 solution, it took a pen, a paper and some 10 minutes, by the feel of it (i didn’t time myself).
October 21, 2011 at 5:35 pm |
Got it! Half an hour with lots of cut out pieces of paper – thank you Richard!
October 21, 2011 at 6:15 pm |
Sounds like something Prolog should be really good at.
October 21, 2011 at 6:22 pm |
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!
October 21, 2011 at 6:56 pm |
And people say that polyamory is a problem.
October 21, 2011 at 7:00 pm |
Took 10min with aid of paper and maybe luck too
October 21, 2011 at 7:57 pm |
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!?
October 21, 2011 at 8:42 pm |
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.
October 21, 2011 at 9:40 pm
These additional restrictions are not true for all possible solutions.
October 22, 2011 at 12:44 am
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.
October 21, 2011 at 10:22 pm |
I can’t even solve this same problem in real life…
October 22, 2011 at 10:33 am |
I think the Smoke Monster loves Arthur.
October 22, 2011 at 1:58 pm |
I Love Lucy!
October 22, 2011 at 2:18 pm |
I’m not sure but I think this was on Gossip Girl.
October 22, 2011 at 5:11 pm |
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!
October 22, 2011 at 8:29 pm |
there is at least one answer, which does not require a graph and is as easy as 22/7.
October 23, 2011 at 4:20 pm
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.
October 23, 2011 at 10:03 am |
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.