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        riddles >> hard >> Re: The Mirrored Maze
        
(Message started by: Ulkesh on Apr 14^th, 2003, 10:28am)

Title: Re: The Mirrored Maze
Post by Ulkesh on Apr 14^th, 2003, 10:28am

...
[hide]
The only way the statements are consistent are with these answers:

1. F
2. T
3. T
4. T
5. F
6. T
7. T
8. F
9. F
10. F

From statements 4 and 7, the number needs to be divisble by 2, 3, 4, 5, 6 and 7. The lowest number that is divisible is 7*5*3*2*2 = 420. Statement 9 is verified as false as the sum of the numbers of the true answers is 22, and 420 has ((2+1)*2*2*2) - 2 divisors (not including 1 or itself) = 22

So the answer is 420
[/hide]

Title: Re: The Mirrored Maze
Post by Ulkesh on Apr 14^th, 2003, 12:54pm

...
[hide]
If statement 1 is true, statement 2 can neither be true nor false. Therefore statement 1 is false, so 2 must be true. 1 being false also implies that 9 and 10 are false.
6 can't be false as it requires itself to be true, so 7 and/or 8 is true. By simple inspection 7 and 8 can't both be true, so one is true and one false. By similar inspection both 5 and 7 can't be true. Therefore the three consecutive true statements required by 10 must be between statements 2 and 6. Threrefore 4 is true.

This gives: F, T, ?, T, ?, T, ?, ?, F, F

If 8 is true, 7 is false, therefore 3 is false and 5 is true. 8 requires the answer to be a multiple of 10, and 5 requires it to be 25, so that's wrong. Therefore the only viable answer is for 8 to be false, 7 true and 3 true. Simple inspection then shows that if 7 is true, 5 must be false. This gives the sequence of trues and falses as in my first post.
[/hide]

Wow... we both seem to be living on the boards today... ;)

Cranial echo, eh? :P What's wrong with my answer? I think it all makes sense.... withstanding any logical pedantry on the part of the clues. e.g. is it logically possible for 6 to be false? I assumed not.

Title: Re: The Mirrored Maze
Post by Ulkesh on Apr 14^th, 2003, 3:57pm

I've been through my answer again, and I can see no obvious errors. I'm afraid I'll need a bit of assistance beyond looking for unjustified assumptions in my hairless assertions... does anyone have any ideas?

Title: Re: The Mirrored Maze
Post by Ulkesh on Apr 14^th, 2003, 5:20pm

on 04/14/03 at 12:34:01, THUDandBLUNDER wrote:

After this, what primitive thought processes, if any, reverberated through your cranial echo chamber while you worked out the unique answer?

After thinking about it, I'll assume you're joking, but, and I mean this in the friendliest possible way, I could have very easily taken offence from that.

By the way, I'm now convinced that my answer is correct. I challenge you to prove me wrong. I'm curious as to why you are so derisive of my workings when you don't seem to know the answer yourself.

Title: Re: The Mirrored Maze
Post by Icarus on Apr 14^th, 2003, 7:46pm

Quote:

If statement 1 is true, statement 2 can neither be true nor false. Therefore statement 1 is false, so 2 must be true.

Since 2 must be either true or false, 1 must be false. But that does not mean that 2 is true. Since 1 is false, 2 is not the first false statement, and is free (on the basis of these two statements alone) to be either true or false.

T&B - It's time to take your Valium. There is no need to get nasty with other posters just because you believe them to be mistaken, and they refuse to admit the mistake. Everyone does that, including you.

Title: Re: The Mirrored Maze
Post by Chronos on Apr 14^th, 2003, 10:32pm

Another potential problem with Ulkesh's solution: Statements 7 and 8 are not necessarily inconsistent. It's possible that the number to be found has both properties.

Title: Re: The Mirrored Maze
Post by THUDandBLUNDER on Apr 15^th, 2003, 1:05am

Sorry, Ulkesh, I did fly off the handle a bit. No personal insult was intended. :-[

Quote:

T&B - It's time to take your Valium. There is no need to get nasty with other posters just because you believe them to be mistaken, and they refuse to admit the mistake. Everyone does that, including you.

Icarus, I find it difficult to understand how anyone can, using faulty logic, arrive at the correct truth values and get the right answer to a complicated problem in just one hour....without using some artificial aid.
That's what I was getting at.

(While it's true Thud has been known to Blunder, he does not refuse to admit his mistakes.)

Title: Re: The Mirrored Maze
Post by towr on Apr 15^th, 2003, 3:10am

on 04/15/03 at 01:05:42, THUDandBLUNDER wrote:

Icarus, I find it difficult to understand how anyone can, using faulty logic, arrive at the correct truth values and get the right answer to a complicated problem in just one hour....

Actually, most people solve complex problems correctly using faulty logic every day..
Living is quite a complex problem, and most underlying assumptions people use are wrong strickly speaking, but nevertheless give correct results most of the time..

So for instance "Statements 7 and 8 are not necessarily inconsistent", but it is probable they are, and assuming they are can help you find the correct answer, and once you have an answer it's easy to validate it.

Title: Re: The Mirrored Maze
Post by Ulkesh on Apr 15^th, 2003, 3:53am

on 04/14/03 at 19:46:15, Icarus wrote:

I agree, It means that 2 can be true or false. However, given that statement 10 is false, statements 2, 3 and 4 all have to be true (3 consecutive true statements). I should have been clearer.

Also, 5 and 7 can't both be true because the number would then have to be a multiple of 3, 5, 6 and 7, at least (according to statement 7). 2*3*5*7 = 210. And the sum of the numbers of the true statements can't be that high as 5 requires.

From an earlier post of mine...

on 04/14/03 at 12:54:53, Ulkesh wrote:

If 8 is true, 7 is false, therefore 3 is false and 5 is true. 8 requires the answer to be a multiple of 10, and 5 requires it to be 25, so that's wrong. Therefore the only viable answer is for 8 to be false, 7 true and 3 true. Simple inspection then shows that if 7 is true, 5 must be false. This gives the sequence of trues and falses as in my first post.

You may ask, why do the three consecutive true statements have to be 2, 3 and 4? Why can't 2 be false? Well, I've established that 5 and 7 can't both be true, I establish below that 7 and 8 can't, so the consecutive statements must be between 3 and 6 (assuming 2 is false). From above, if 8 is true, 7 is false, therefore 3 is false and 5 is true. 8 requires a multiple of 10, and 5 requires an answer of 23 (as 2 is now false). This is wrong.
Therefore 8 is false, 7 is true (as 6 requires it), and 3 is true. But 5 must be true as 3 consecutive true statements are needed. 7 and 5 can't both be true, therefore 2 has to be true. So the consecutive true statements must be 2, 3 and 4.

on 04/14/03 at 22:32:12, Chronos wrote:

Another potential problem with Ulkesh's solution: Statements 7 and 8 are not necessarily inconsistent. It's possible that the number to be found has both properties.

If 7 and 8 were both true, the number would have to be a multiple of 7, 8 and 10 and be 100 or less. 2*2*3*5*7 = 420 (same as the original answer... wierd!). Anyway, 420% of the answers can't be correct.

Anything else to clear up?

Title: Re: The Mirrored Maze
Post by Ulkesh on Apr 15^th, 2003, 3:32pm

on 04/15/03 at 01:05:42, THUDandBLUNDER wrote:

So, does my answer have your approval yet, O Wise One? ;)

I've tried to plug the small gaps I didn't explicitly explain, but I think I've proved that my reasoning was correct from the start. As as for using artificial aids, the puzzle isn't that difficult. It just involved making sense of the locations of the trues and falses, then it was simple enough to find the correct value.

By the way, given statement 9, no multiple of my answer is valid. Therefore I think that [hide]420[/hide] is the only valid answer.

Title: Re: The Mirrored Maze
Post by THUDandBLUNDER on Apr 25^th, 2003, 7:56pm

Hi Ulkesh. Haven't seem you around for a while. Exams, huh? Here is my solution:
[hide]
Either
2 is True; in which case it is the first True statement;
so 1 must be False,
OR
2 is False; in which case it cannot be the first False statement;
so 1 must be False.
In both cases, 1 is False;
therefore 9 and 10 are both False.

Assume 6 is False. Then it must be the last True statement, which contradicts the assumption that it is False;
therefore 6 is True.

Either
3 is True; then 8 is False; hence 7 is True because 6 is True;
so {by 7} the number is at least 42.
OR
3 is False; then 2 and 8, and either 4 or 5 are True; together with 6, at least 40% are True;
so {by 8} the number is at least 40.
But the sum of the sum of the numbers of the True statements is at most 35 (because 1, 9 and 10 are all False;
therefore 5 is False.

Assume 3 is False; then 2, 4 and 8 must be True;
but then 4 implies that the number be a multiple of 6;
and 8 implies it is a multiple of 10, no greater than 50 [because we 'know' 1, 3, 5, 9, and 10 are False];
as this is impossible, 3 is True.

3 is True implies 8 is False and 7 is True

10 is False implies 2 is True and 4 is True

Therefore 2, 3, 4, 6, 7 are True.

LCM of {2,3,4,6,7} = 84

But (by 4) number must be divisible by 5.

Therefore number is 84*5 = 420 [/hide]

Title: Re: The Mirrored Maze
Post by Margit Schubert-While on Jul 2^nd, 2003, 5:34am

I think this is bogus. It's discussed at the below link about half way down the page.

http://www.faqs.org/faqs/puzzles/archive/logic/part1/

Title: Re: The Mirrored Maze
Post by Dante on Jul 3^rd, 2003, 7:48am

Margit, the argument at the link you posted seems to be that we cannot assume that all the statements in the list are either true or false - some can be meaningless.

However, T&B's post starts "Below are 10 statements, all either true or false". I think this invalidates the argument, and makes this riddle perfectly valid.

Title: Re: The Mirrored Maze
Post by James Fingas on Jul 3^rd, 2003, 8:03am

Of course, T&B could be lying when he says that. However, it's still an interesting puzzle to see if you can make it work out. Some lists of statements could never work out. Example:

1) At least one of these statements is false
2) At least one of these statements is true

It's similar to the python riddles: of course the statements could be meaningless, but then we wouldn't even bother to try and figure it out. And that would be no fun!

Title: Re: The Mirrored Maze
Post by zero on Jul 12^th, 2003, 4:53pm

on 07/03/03 at 08:03:33, James Fingas wrote:

well i still dont get it you guys are ignoring facts some of you are saying the first one is false but there are atleast one true statement