Critical Thinking: Three People Puzzle
November 6, 2009 by Dr. Steve Bedwell
Filed under Critical Thinking
Robin Cervantes commented today on a puzzle I posted a while back: Critical Thinking – Bus Puzzle.
Here’s another puzzle I came across recently which demonstrates a specific error we make when trying to solve a problem. (It’s adapted from the work of a computer scientist at the University of Toronto called Hector Levesque):
- John is staring at Jill, but Jill is staring at Jack.
- John is married, but Jack is not.
Question: Is a married person staring at an unmarried person? Multiple Choice Answer:
- A. No
- B. Yes.
- C. Can’t be solved with the limited information given.
Hint: Don’t get distracted by the cute duck picture. I added that because it was, well…cute!
When we have ten answers (or suggestions of how to proceed) in the “speak your mind” box below, I’ll tell you the solution. I’ll also explain the thinking behind it and what it reveals about one of the errors we make when we try to solve a problem.
Good luck!
All three answers are correct.
Hi Mark,
Thanks for playing
Cute ducks, don’t you think?
I need a little more explanation on all three answers being correct?
From my viewpoint, using the data you’re given only one answer is correct. Here’s a hint: Look at one of the people from more than one perspective.
Ask some of your wonderful colleagues, see what they have to say.
I think c. Can’t be solved with limited information given. The duck picture appears to lead the eye to see the two ducks with ties as male and the one in the middle is female. while it may be a fare assumption, it is not one that I would base an answer on. Go Man. U!
c: I do not have the marital status of Jill. John is married and staring at Jill, whose marital status is unknown. If they were all standing in a circle, they coould see each other, but “staring” implies at one person, not peripheral vision seeing the others.
The ducks are very distracting….
I think that Jill is married to John…that is why she is staring at Jack.
I Think it’s “C” as we do not know if Jill is married.
Wow! Thanks for all the input. As soon as we get to 10 suggestions (not including my replies…yea, I’m playing hardball!) I’ll tell you the answer…Which, as a Perspective Power team, we have yet to figure out.
Here are some clues:
.) I suggest you scroll down your browser window until the ducks (and my picture) are hidden.
1. There’s a lot of duck-related confusion. The duck picture is purely to punch up the cute factor. And when it’s my picture at the top of the blog, trust me I need all the additional “cute” I can muster! (Feel free to disagree
2. The “Three Person Puzzle” can be categorically solved (leaving you without any doubt that you’ve figured it out) using the data given. It doesn’t require any additional information hidden elsewhere on the page.
3. Look at one of the people (or, if you insist, ducks) from more than one perspective. Sandie and Theresa’s comments are accurate, but their conclusion is wrong.
4. The people are orientated in a line (just like the ducks) with Jill in the middle. And, Julie, I have no idea if “Jill the Duck” is happily married, unhappily married…or even unmarried (and dating both John & Jack).
Dean, thanks for noticing the absence of a tie…which took me a while to Photoshop out. No clue to the puzzle, just that I had too much time on my hands yesterday. And clearly if the ducks were Man United supporters their ties wouldn’t be blue and white…the colors of Chelsea Football Club!
I await further input with interest. Thanks for playing,
Steve
Yes. Jack can still see John past Jill.
I’m going to go with A – No. Just because it doesn’t appear to have been selected.
Hey Bob,
Nice to hear from you. And Julie, we’re up to seven comments. Rope in a couple more members of your family (and maybe the dog) and I’ll reveal all
There is a solution to the problem, using nothing more than the information given, which doesn’t rely on peripheral vision or adulterous ducks. This solution also provides what psychologists call a “cognitive snap”. An awareness that you’ve found an intellectually satisfying answer.
I’ll repeat my mega-clue: Look at one of the people from more than one perspective. Sandie and Theresa’s comments are accurate, but their conclusion is wrong.
Bob, I’d be interested to see what your students make of the Three Person Puzzle.
Enjoy the rest of the weekend,
Steve
Osa, the puppy, thinks all of the ducks look like dinner and she believe she can catch them! She is afterall a bird dog!
Julie,
Is it just me, or are you not taking this seriously
OK, after much thought, a sleepless night and a final consultation with my 3 and 6 yr old, I believe the answer is B. Jill is the only person whose marital status is not known, so she is either married or unmarried. If she is married then the answer is Yes, she would be the married person looking at an unmarried person. If she is not married then the answer is still yes, because John is married looking at Jill (I will not infer what he may be contemplating while starring at her).
The bigger question, from my 3 yr old is how do the ducks keep their sunglasses on if they don’t have ears? Another sleeples night ahead.
By the way ask Julie about the letter.
John is starring at Jill (his wife), who is starring at their baby she is holding, Jack.
Yes, a married person is starring at an unmarried person; as Jill is starring at her son Jack.
Interesting idea Sandie, and Dean…You’ve cracked it! Your answer and reasoning are a truly brilliant example of consciously reframing a problem from opposite points of view. (Honestly, with such genius, Man U. deserved to win!)
When we’re trying to solve a problem, one of the most effective things we can do is ask the question: What am I missing? And then mindfully flip our Brain-Frame every which way; looking for Outside Insights…You did this, full kudos.
The reason I posted the “Three People Puzzle” is to show how, if we’re given an out (C. Can’t be solved with the limited information given) we take this path too quickly. We stop thinking too soon and, as a result, miss clues to better solutions. The secret is to mentally ‘bracket-off’ our first answer, and keep looking for the second, third and fourth “right” answer.
In other news: I’ve just posted the second part of my “Mistakes Executives Make Managing Change” series, I would love everyone’s observations on these ideas. No puzzles, no ducks…just powerful tactics for managing change.
http://www.stevebedwell.com/bl.....istakes-2/
And, as for your 3 year old’s question re: the duck’s ears. What a great observation! This is precisely the kind of thinking we need to rediscover as adults. I take off my hat to her/his natural creativity, superb! (Obviously a Chelsea supporter.)
Have a great week,
Steve
PS: Julie, what letter?
We may have solved the puzzle, but Man U lost, so what are we going to do to gain back the 5 points in which they now trail the despicable Chelsea.
“what are we going to do to gain back the 5 points in which they now trail the despicable Chelsea.”
…Call me simplistic, but you could try winning
Be on the lookout for the next Perspective Power message tomorrow. I’m looking forward to hearing your opinions…
Steve
If this problem were posed by a computer scientist, I would use logical
disjunction and come up with for “B”. But with the hint asks me to look
at the problem from several perspectives. Since I am no cognitive miser,
I exercise my imagination and have to say that the answer is C:
• The _title_ uses the word “people”, but the problem never
indicates that Jill is a person. If Jill were a goldfish
or an alien or a statue, there might be no instances of a
person staring at another person amongst John/Jack/Jill.
But there might be. Thus, the answer is undeterminable.
• The conditions say Jack is not married, but they do not say
that he (or anyone else) is unmarried. In some contexts, the
two terms do not have identical meanings. The person posing
the problem could have made it unambiguous, but did not do so.
Thus, the answer is undeterminable.
• Married according to whom? Jill civilly marries her lesbian
partner Joan in Iowa and the couple then moves to Mississippi.
A few years later, they seek a divorce. John, their attorney,
is looking at Jill. Jill is looking at the unmarried judge,
Jack, who is just about to rule in the case. The answer cannot
be determined.
Finally, the statement of the problem does not restrict its domain to
John, Jack, and Jill. Because there is indeed somewhere in the universe
a married person staring at an unmarried person, the answer is B — but
not as a consequence of the problem’s conditions.