**By Louise Mayor**

Welcome to the second instalment of the Physics World at 25 Puzzle. The first puzzle was released last week and your second challenge lies below. #PW25puzzle

Is Schrödinger’s cat alive or dead?

1. Schrödinger’s cat is alive.

2. Schrödinger’s cat is dead.

3. Exactly one of statements 6 and 9 is true.

4. Exactly one of statements 2 and 6 is false.

5. Statements 4, 5 and 10 are all false.

6. Exactly one of statements 1 and 10 is false.

7. Exactly 5 statements are true.

8. Exactly one of statements 3 and 10 is false.

9. Exactly one of statements 6 and 10 is true.

10. Exactly one of statements 1 and 2 is false.

11. Statements 1, 8 and 11 are all false.

Enter your answer as a list, in numerical order, of the number(s) of the statements that are *definitely* true, as a single string with no spaces, such as, for example, 25811.

Enter your answer here

So that others can enjoy the puzzle too, please DO NOT post the answer in the comments.

Feel free to discuss the puzzle as long as you do not get too specific. You can check whether your answer is correct using the box above. Happy puzzling!

Really annoyed by this puzzle as the system refused to acknowledge my answer as one of the two correct answers.

After multiple checks I realised there were actually two correct answers, put in the other and it was confirmed.

Funny, I am the 1421 person who solved this riddle. If you have solved it as well, then you will know why it’s funny =P

Considering the question carefully I have found a third valid answer. The firstmatches the official answer. The second is the variation the puzzle builder missed. But there is a third answer – and you will love it ! !! !!!!

Good job Jeffery! … If you ultimateley reach the conclusion that there could be 11 [ELEVEN]possible right answers – one of my answers must be right! ..Still struggling 2 days in

Now I KNOW I know nothing about physics… how can I post a reply to the above post BEFORE he’s posted it! ???

I am totally convinced there are no more than the 3 answers, and can only be considered if you allow the cat to be both dead and alive at the same time

looks like I have to scratch the third answer as I found one error when testing in the morning (I guess I rushed to post too soon on this one). The other two answers are still valid though and have passed all testing.

Yep, solved it in several minutes!

loving the whole ‘check it & the answer changes’ bit, but don’t think i’m close to solving it. this is better than last week’s

5th person…bring on Puzzle #3!

Well, that had me thinking in circles! (Literally, actually, as I found using a Venn diagram to be quite helpful…). 10th person to get it, too, which is nice.

I have another question and it is, if such puzzle is quantum mechanic equations if made correctly. And if we make another sort of Schrodinger´s cat puzzles if it is another set of quantum equations?

I am sure there are two correct answers! -Depending on #7… right?!

Agree. Nice of you to give a big clue to anyone reading the comments

No

Remember is asks what statements are DEFINITELY true. A statement that depends on itself for validity is conditional and therefore not definitely true.

Easier than last weeks – lucky 13!

@Garth…read the question!

Number 21! Garth I agree it hindges on 7 so there are two right answers no?

Great puzzle! had a lot of fun with this one

20th person

If you keep the italicised emphasis in the question to mind, it becomes much easier!

Person no 29

Person no 27

#30th – but over an hour after publication

phew! number 35…was thinking about it way too hard, apply simple logic and it all falls into place.

Last weeks took me hours (although that did include a crash course in basic cyrptology at simon singh’s website), yet this one I found quite straightforward. I suspect that although my woeful lack of physics knowledge hindered me slightly last week, it is perhaps an advantage this time…

I am totally confused

the fact that schrodingers cat can be both alive and dead is confusing!

42!!!

*geeks out*

No.45

Is it right that if, say, exactly four statements are true, then statement no. 7 must also be true making five? or is this not logical?

That’s actually a very good question…

Yes that is perfectly logical which is what I had first.

I like to think in that case, statement 7 is both true and false at the same time. It is in a superposition that only collapses when you submit it.

#54 – i thought i was right so many times before that i’m not sure i could get it right again, but made it – more brute force than logic though :-/

Took a while and a spreadsheet but got there at number 60. Though I agree that 7 suggests two answers and I can’t see a logical distinction between them!

Just spotted why only one answer.

definately true. Doh!You still need to fix the website so that Ithe count does not accept multiple correct entries from the same computer or phone.

Thanks that made me think for a bit. A slow 69th.

I was 74th, though I still worry about my logic.

#76 pleased with this! Just wondering though if one of the false statements is self referential (last one evaluated) as I originally had this as true which was wrong.

no 97 took about 20 min

Hang on, is this supposed to be in the framework of the Copenhagen interpretation .. i.e. can Schrodinger’s cat be both half-alive and half-dead?

Or is it supposed to be a traditional logic puzzle where statements can either be true or false and cats can either be alive or dead but not something in between?

And what about the many-worlds interpretation?

It is purely a traditional logic puzzle. I think the original introduction to these 5 puzzles said that they could be solved with logic and without detailed knowledge of physics. Don’t try to make it too complex!There is only one correct answer that is logical.

Exactly where did it say that physics was irrelevant to the solution to these puzzles? Schrodinger would be appalled, if true.

Nice puzzle for Nobel Prize announcement day! #106

OK, a little uncomfortable with this one.

Schrodinger’s cat is supposed to be both alive AND dead. This puzzle sets it one way or another, (I won’t reveal which, #51).

You mean ‘None’ is not the correct answer – seeing as yes-no statements about the world cannot be *definitely* true in QM?

Shame! We need a quantum logic puzzle!

Forget about Schrodinger. Call it Smith’s cat then there is no problem with QM.

I agree with Cherokee, without revealing the answer, I don’t like the answers to 1&2.

assuming you look to find out then surely it could be one OR the other, and if you don’t look, then it could be either.

You either know with certainty and it is one OR the other, or you DON’T know with certainty and therefore it would be neither…

Not convinced.

me too – and spent so long assuming one or the other… :-/

#114-

128th, I agree that there are must be 2 answers.

136th. Lunch break scrambling to get that done before I had to clock back in.

Number 168.

Great puzzle!

I would also say there is another possible solution that meets the requirements of “tatements that are definitely true”.

#177, took about 10 mins. Nice bit of deduction involved. I liked last weeks too, again about 10mins, #4876. It was fun seeing the message appear before your eyes, word by word. There is only one answer that is definitely right.

Didn’t like it. Not only does it assume classical physics (ie the cat is either one or the other, not both), it seems to require you to deduce something using statement 11, but 11 is a Cretan paradox from which nothing follows except that it can’t be definitely true.

‘This sentence is false and Statement 1 is true’ has exactly the same content as ‘This sentence is false and Statement 1 is false’ … neither give you any information about Statement 1.

stringph I didn’t use statement 11 to try and determine the truth or falsehood of statements 1 and 8. I started with the cat! You might have found this easier if it hadn’t been labelled ‘Schrodinger’s cat’!

Is this a logic puzzle or do you bring meaning from the outside world? Statements 1 and 2 say nothing on their own but have to be evaluated in terms of the other statements. They are independent. Could have said Schrödinger’s apple is red, Schrödinger’s apple is green, then red and green can exist together. You can still evaluate the logic. Having alive or dead in there is bringing in outside knowledge beyond logic as is cat.

That’s exactly what I did. And then applied a bit of ‘Conan Doyle reasoning’, ie once you’ve removed everything that’s false then whatever remains, however improbable, must be the truth. Also, I didn’t let any quantum theory cloud my thinking, which seemed to work.

Who said it was hard? Not when treated as a traditional logic puzzle. But if you ignore 11 (because it’s self-contradictory) you can’t get the ‘right’ answer.

Statement 11 like 5 can be evaluated. They could lead to a paradox but in this case clearly don’t. Can’t say more without giving too much away. The ambiguity though is around #7.

I agree with Andrew W. When you follow the logic, statement 11 is as solvable as statement 5. Also, the question asks for the numbers of statements that are ‘definitely true’, not those that can be true or false, which seems to have confused some people.

Agreed.

I initially thought the setters were being clever by allowing 2 answers. However only one is accepted for submission, and both give the same outcome for the cat. Think they have screwed up with this one.

I’m sorry if I cannot find the screw, but looking for non subatomic certainties -which is what this puzzle is about- it’s very easy to find only one right, straight solution.

I’m sure I’m not the sharpest tool in the shelf, but this is a very good puzzle for having some relaxing fun!

#197 – Seems that the solution requires as much philosiphizing as logic. I had to make certain assumptions that I would have preferred not to make in order to arrive at this solution.

It appears there are more than 1 way to skin a cat!

Has anyone spotted if there is, like the previous puzzle, an underlying meaning to the solution? e.g. does it represent a significant date?

204

Took a while this one as thought too deeply re 1 and 2!

#150, but I’m not satisfied by the answer, even if the question-master is. I look forward to seeing a published solution.

I agree

Got it, finally. Disappointed it wasn’t all crypto though!

I agree that this puzzle wasn’t as delightful as the first, but it was satisfying to solve it nevertheless. It took up more paper than the last one, too (I tried using a computer but the spreadsheet software I used didn’t like self-referential formulas!) I came in 123rd, and it took me probably an hour all told (I was doing it in snippets of time throughout the day).

Number 274 and now my head hurts even though it took me about 10 minutes.

Number 278. It took me about 20 minutes! That’s not good.

I agree with Cherokee on this: there are degenerate solutions, although only one is recognised as correct. Presumably once the answer was fixed, no other outcome was possible …

Interestingly, the solutions do have common factors that strictly satisfy the question. I spent a long time worrying why it was incorrect and think it makes a much more satisfying answer.

Does anyone else think the cat’s fate could be different from the one implied in the answer?

My head hurts now. Number 341 and it took me 30 minutes!

346 Yeeeeeey!

When you really boil it down there is only one possible answer. Took me a while but now I see the light

No.611. Once I got the Multi-worlds Interpretation of the Copenhagen Principle out of my head it became simple.

Person 622, took a while, not satisfied with the answer (agree with Catweazle above) and the earlier comments about Statement 7. Once I challenged some interpretations, worked through it. Will ponder some more, but look forward to seeing a worked solution…

#630

Easier than puzzle 1

Fortunately there’s only one state for the cat.

I’m #662 nice game, need more

268th – like others, I’m not entirely convinced on the state of this moggy. Any elegance or wit to the solution went straight over my head.

#867, really tricky at first but after understanding the problem you go straight to the solution.

#876, principally because I forgot about the puzzle until it had been live for 8 hours Doh! Was worried it would be a harder cypher this week which would have certainly stumped me! Thanks Louise.

If you google the answer as a date (you have to include the wrong answer for statement 7) then you do get a significant event in Quantum physics observations! Was this deliberate?

Only one solution is the right one (watch out the phrase definitely true)

#983 Got it after a few minutes but couldn’t complete it till just now as ive been at school. I think there are two different solutions with different outcomes for the cat but there are some statements that must always be true and some that must always be false

#1022, I tried a variety of ways to solve, with network diagram and random trial and error, finally spotting the route through the maze. I really enjoyed this one, looking forward to the next challenge.

#1048, woo This was a tricky one. My head hurt after a bit, but you’ll all get it eventually!

1063- I had the right sequence, but statement 7 is very deceptive and so it took me quite a long time, for such a simple puzzle. Btw I am supposed to be a Phd at Imperial.

Logical simplicity comes first, my friend.

For those unable to solve this, fear not. If you don’t enter your answer it surely lives in a state of both right and wrong

1071st. 15 minutes to solve. Agree with references to Sherlock Holmes before, deductive reasoning and experimentation are the keys to solving this puzzle.

#1080 – ah…if I hadn’t made a silly mistake with one of the statements I would have solved it within minutes. Nice one Looking forward to the next puzzle!

Sam has it in a nutshell. Unfortunately, this leads to a different solution to the one which is expected.

Took me a while to figure it out, a grid and 3 assumptions. then I was unsure about 7 so tried with and without before succeeding. no. 1128

I’m truly disappointed with this puzzle. It’s more about brute force than about physics or logic. And still not convinced at all that there’s only one solution.

The second -or first- solution you mention is not possible due to it has not happened before, so it cannot be true a priori. Junior High School Physics Teachers rule! (:

I mean, in our own dimensional experience, that is, of course…

#1137 and less than 5 min!

Interestingly, there is a unique solution for which the cat can be dead, alive, or in a quantum superposition of the two states. Once the cat’s state is determined, the answer changes, but you need to know whether it is alive or dead to get the solution which the puzzle is looking for.

#1118

Statement 11 is the key to solving this. The cat can be in one of 4 states (alive, dead, both or neither). For only one of these can the state of statement 11 be deduced, therefore that’s the correct state of the moggy.

In my modest opinion, this second puzzle is easier or, at least, as easy as the first one. Hope the next one will be a hard challenge for all the fans!

You thought the first puzzle was easy???

Respect.

So sorry about that but in my honest opinion both puzzles were pretty easy for me. Maybe I’m used to solve puzzles and they were more hard for others to solve.

I think there another solution 2,3,6,10. Can someone else check this for me.

2 3 6 10 makes 1 and 8 false and 11 therefore becomes a paradox. I think that’s the crux of the “correct” solution, though to me it seems like a case of the tail wagging the dog (or should that be cat).

Thanks

The bloody cat’s been in the box for 78 years now – of course it’s dead! :-/

Number 1198. Break it down.

The solition to this question has just opened my eyes to a world of brand new possibilities.

1. I will win the lottery tonight.

2. I won’t win the lottery tonight.

3. 1 and 3 are both false.

WOOHOO!

Statement 5 says statement 5 is false – this is like saying you are lying: are you then telling the truth, in which case you are not lying, in which case the statement is false, in which case you are lying…etc….

Statement 7 is true if you include it in your ‘true’ list, but false if you include it in your ‘false’ list – both ways appear correct to me.

Its all be said before.

Nothing to add apart from the fact that my Haynes workshop manual for a Mark IV Large Hadron Collider was of no use whatsoever. That is going back for starters. Oh, and my ordinal number isn’t even a prime, a square or anything.

Heck, I’ve just looked at it agin and its changed ……..

No: 1382.

Didn’t take me as long as the first. Roll on next Tuesday. Be great if they did one everyday.

#1403 I thought Last weeks puzzle was fun, but this one was fairly unsatisfying. I tried to use logic from the start to sort it out and was getting nowhere. Then I made an assumption (which I hate to do in logic puzzles) about the cat, and solved it in seconds.

1419th person

I did it using Truth Tables

Well, I make that 111 comments. Seems like some people prefer puzzles to physics. I don’t have time for this sort of thing I’m afraid. Especially since Schrodinger proposed his cat to demonstrate that the Copenhagen Interpretation led to a nonsense scenario. And it’s since been hijacked by quantum mystics.

If there are quantum steps, then also particals spins have character of such quantum steps?

Person Number 1451.,

Nice Puzzle!!

#1458 (I think) – ended up drawing a circuit diagram and twiddling the inputs on paper!

Q7 is still making no sense to me and caused a lot of wasted time yesterday testing the both alive and dead / neither possibilities before forcing the issue and taking a punt. [yes i should have read the comments first] Anyone explain Q7?

Its vague but maybe “definitely true” means that the puzzle is valid only if that question is true and it only gives a valid answer to the puzzle when true and not when false. The puzzle is valid if q7 is true or false. So as we have a valid puzzle when q7 is false rules out that question being included in the exclusively true count. Or to paraphrase ‘true and only ever true case’.

I understand the Statement 7 conundrum…but I still get 2 ‘valid’ answers. The ‘officially’ correct version and the other one, mentioned above. As far as I can see they both work (maybe that’s the point!!). Also, regarding Statements 5 & 11, as they have only one possible (non-paradoxical) answer, neither gives any useful information about any other statement.

Statements 5 and 11 do provide more information than you think, but it would not be fair to discuss what that is right now as others are attempting the puzzle.

I would love to discuss the solution with you all, but for now my mouth must remain zipped! The solutions will be revealed, but not until everyone’s had a good chance to have a go at all the puzzles. I’m really pleased that people seem to be enjoying/squirming as much as I did at various points throughout the puzzle testing. Not long now till Puzzle 3….

I am number 1608. For me it took almost a day, but anyway its happy ending..

Terrible puzzle, the wording of the question very clearly leads to statements 3, 4 & 10 being the only ones that are *definitely* true. The cat is neither *definitely* alive or dead according to the statements made. If you start making assumptions about the health of the cat there are, in fact, 4 possible answers. Please do better next time Louise.

@bod your statements are completely false. Simple logic, the puzzle prompt “Is Schrödinger’s cat alive or dead?”, and statement 10 “Exactly one of statements 1 and 2 is false” (which you said must be true) clearly mean that #1 and #2 CANNOT both be true. Therefore one statement MUST be true and the other MUST be false.

Victoria – your assumption that the cat cannot be both alive and dead is as suspect as an assumption that someone cannot be in many places at the same time, or that an event in the present cannot affect an event in the past – it’s quantum physics, and the cat is a quantum physics subject.

I need to start trying these the day they are published. Both puzzles from last week and this week only took me a few minutes. It is currently just past 12 EST and the forum shows 5pm so I’m guessing these are published around 5AM EST on Tuesday?

1638th to get it right! Took me a lot longer than it should have!!!

Number 1650 here. Took about 20 minutes – after I got over #7!

I am number 1659 yey

Fun puzzle

#1669

This is not a logic puzzle. It is a joke… an Andy Kaufman style joke. Start with the result you hope for work it out from there and it will take minutes. There are at most two possible answers this way. If you start with the facts, you will be sorely dissapointed. #1688

Got it #1703 took about 1/2 hour, forget the question is about Schrödinger’s cat and it is just step buy step logic

Got it #1757 a couple of false starts but got it in the end.

It asks which answers are *definitely* true. For as long as I’ve been thinking about it, there are only 3 I could see as definitely true.

Having now submitted the “correct” answer, I still say there are only 3 that are definitely true.

I think we may have been through the same thought process, as I came to that conclusion as well.

If so, it’s statement 11 which leads to the rest of the answer.

It certainly help.

Paradoxical statements are always handy, if only to narrow the field.

I did it using algebra, I wrote each statement as an equation, then simply substituted and reduced until I was left with a definite set of true / false values. Quite fun, took me ages to realise this was the technique.

person no 1827

tricky one

I entered 6 wrong answers :p

and now my heart is racing..

After an incorrect guess should I refresh the page or does it recognise a second attempt as a new answer?

Took me about 10 minutes using pen and paper. No diagrams or functions or anything, just 13 bullet points with T/F behind them, the rest was brain gymnastics.

Disappointed with this one. The answer is completely arbitrary, to figure it out you essentially have to lower your wisdom to that of someone who has no clue what the schrodinger’s cat thought experiment was meant to demonstrate, and then gamble on one of 4 correct answers (you cannot make definite statements about an unknown, and therefor you cannot even assume that the answers to 1 and 2 are opposite, hence 4 possibilities, not 2).

The only actual correct answer is the one answer you cannot enter: none of the statements can be said to be definitely true.

Nothing arbitrary and no gambling required, just logic. I think Schrödinger’s cat is more of a Cheshire cat smiling at what our macro world would be like if it followed the quantum laws. This is a good puzzle very much in the spirit of the quantum as they both make people uncomfortable. Just glad that this weeks problem “cohered”

#1921 Got there eventually by using a binary tree.

Only got a b at o level gce but managed both puzzles 1 and 2.

1936.

annoying…

alive and dead are entirely classical (NOT quantum).

use the obviously correct answer for 5 to decide for 11.

It sort of irked me that supposition was required to solve this puzzle. You had to “guess” at least once before logic came in to play.

Without getting into spoilers, it took me much longer than it would have if the subject had been something other than that feisty feline.

Went throught it twice and got same answer. I guess that the number that is true and false represents the cat.

Number 7 is silly.

Schrodingers cat: What if doesnt exist observer outside box? Will cat be live and dead forever? We can go outside our universe and suppose that there doesnt exist observer. So outside our universe is cat live and dead forever??

What does it mean?? From this we can say that if we are not able observe particles or matter then this matter is in superposition and we cant say about more its qualities. But maybe we can observe just one part of its qualities ( that this matter is partly in superposition and partly is wave function colapsed ). This is case of dark matter.

I have thoroughly enjoyed the first two installments, patiently waiting on the third…

Thanks for these puzzles – gives a few minutes of hard thinking – something i haven’t done since i was at Uni….

Yes, thank you for setting these puzzles. The first two have been very satisfying to solve and I’m looking forward to the third one tomorrow.

If the question is, “Which statements can only take the value true, when the whole set of statements is self-consistent?” then neither of the potentially paradoxical statements can be paradoxical. I started from there and the required answer (which is the only correct answer to the above interpretation of the question) follows.

If you think “paradoxical” is a different intrinsically consistent state for an individual statement, then the answer is, “None of the statements is definitely true. (But there are some which are definitely false).”

If you are still stuck this may help:

1) Pretend it’s your cat.

2) Guess Q1

3) Answer the rest in this order:

Q2,Q10,Q6,Q4,Q5,Q9,Q3,Q8,Q11,Q7

4) Enter and see if you have the solution.

5) If not, go back and change Q1 and repeat.

Hint: Think very carefully about Q7……

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Reading through it, I got quite confused. Just wrote a list in sequence, labelling each number as ‘true’ or ‘false’, and worked it out in a few minutes – not quite as difficult as it seems initially.

You do need to think pretty carefully about statement 7, though.

Hmm. Got it eventually (#2107) but only after reading the various comments – especially the hint from Dead or Alive…

Again, I was looking for too much complexity (i.e., from quantum mechanics). Unfortunately, you have to neglect quantum mechanics to get to the answer, and this was somewhat misleading, especially given the way the question was posed…

I do feel slow, though

2625th person, slow!

but still

2626.

Write up some formulae in Excel using boolean functions. Then fill in values for statements 1 and 2.

I’m a bit lost… I have 2 solutions for this, and only one seems to be accepted. I’m not talking about with and without 7, in which case I’d have 4 solutions, but I assume these two would only be acceptable if we were allowing for multiple worlds. I’ll give my second solution here, because it is apparently a wrong answer, so I’m not giving away the correct answer. My second solution is 23610. I wonder if someone coming across this could tell me why this is wrong?

Just to add… I’ve just found C Pearce, and A Wren discussed this possibility further up on the 9th Aug ’13; this second solution makes statement 11 a paradox. But to my mind, this would make 11 neither true nor false, so can basically be ignored since it cannot provide any useful information, making this solution acceptable.