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        riddles >> medium >> Logic: and the answer is...
        
(Message started by: BNC on Feb 2^nd, 2003, 3:57am)

Title: Logic: and the answer is...
Post by BNC on Feb 2^nd, 2003, 3:57am

Each of the following multiple-choice questions has a single solution that doesn't contradict the other answers:

1. The first question with answer (B) is:
A: 2; B: 3; C: 4; D: 5; E: 6

2. The two only consecutive questions with the same answer are:
A: 2 and 3; B: 3 and 4; C: 4 and 5; D: 5 and 6; E: 6 and 7

3. The last question whose answer is the same as the answer to this question is:
A: 10; B: 9; C: 8; D: 7; E: 6

4. The number of questions with answer (A) is:
A: 0; B: 1; C: 2; D: 3; E: 4

5. The answer to this question is the same as the answer to question:
A: 10; B: 9; C: 8; D: 7; E: 6

6. The number of questions with answer (A) is the identical to the number of questions with answer:
A: B; B: C; C: D; D: E; E: None of the above

7. The alphabetical distance between the answer to this question and the answer to the next question is:
A: 4; B: 3; C: 2; D: 1; E: 0 (same answer)

8. The number of questions whose answer is either (A) or (E) is:
A: 2; B: 3; C: 4; D: 5; E: 6

9. The number of questions whose answer is either (B), (C) or (D) is:
A: prime number; B: Factorial number (n!); C: A square (n^2); D: Third power (n^3); E: Number divisible by 5 (5n)

10: The answer to this question is:
A: A; B: B; C: C; D: D; E: E

[edit]
Edited to correct grammatical errors pointed by Icarus
[/edit]

Title: Re: Logic: and the answer is...
Post by Icarus on Feb 2^nd, 2003, 12:33pm

I have a question on interpretation. I know English is not your native language and I think that has led you to mis-state question 3, which says

The last question, whose answer is the same as the answer to this question is:

Well the last question is 10, so the answer to this question has to be (A), and the answer to 10 has to be (A) as well.

But I am wondering if that comma is really supposed to be there. "The last question whose answer is the same as the answer to this question is:" could conceivably be any question from 3 on. This seems to be more in the spirit of the puzzle.

(Small gramatical quibble: 4, 8, & 9 should say "questions" not "question").

Title: Re: Logic: and the answer is...
Post by BNC on Feb 2^nd, 2003, 12:58pm

You are right on all four points, Icarus.
My apologies for anyone who was confused by my errors. Corrections incorporated into the original post.

Title: Re: Logic: and the answer is...
Post by wolfgang on Feb 2^nd, 2003, 2:45pm

The answer: [hide]
1 c
2 d
3 e
4 b
5 e
6 e
7 d
8 c
9 b
10 a [/hide]

Title: Re: Logic: and the answer is...
Post by BNC on Feb 2^nd, 2003, 11:41pm

1. Correct
2. "explaining how you arrived at an answer is more valuable than the answer itself"

Title: Re: Logic: and the answer is...
Post by aero_guy on Feb 3^rd, 2003, 3:19am

OK, you want an explanation of technique, so I will write it as I solve it.

Made a logic puzzle matrix, maybe it will help.

Right off, 1 cannot be B as that is self-contradictory.

Consequence of #2: max of 6 questions with any one answer.

Translating number nine and noting if an answer is repeated in several answers it cannot be correct gives us: A) 3 or 7, B) 6, C) 4 or 9, D) 8, E) 10

Comparing 8 and 9 gives us a possible combination of answers: 8-A 9-D, 8-B 9-A, 8-C 9-B, or 8-E 9-C

Now we compare with 7 and see a possibility is 7-C 8-A 9-D. The second possibility above has no workable answers, 7-D 8-C 9-B is good, and the fourth has them all work, which must be wrong.

Lets work with the first possibility:
As a consequence of our answer for 8, 4 must be either B or C.

By number 2, number 10 cannot be D.

with the answers we know number 3 must be either A or E.

By number 8, none of the rest of the answers (other than 3) can be A or E.

Since the response A is now obviously wrong for number 3, it must be E, which also cannot be right. This is a contradiction, so the correct set must be: 7-D 8-C 9-B. All of a sudden we have three of the answers, now we are getting somewhere!

Unfortunately with this combo 3 doesn?t tell us anything.

by number 2, 10 cannot be B.

OK, now things start to suck. For 3 and 5 B, C, and D are all valid answers, they don?t help at all. Seems 2, and maybe 1 will be the biggest help.

Oh, 4-A is a contradiction and can be eliminated.

Damn, now I have to guess. Try 1-A, gives 2-B, gives 3 and 4 the same. They can?t be A since 4 can?t be A and they can?t be B because that would make 3 B?s in a row. They can?t be E because there are only four questions with A or E as an answer and with two E?s you can?t get four A?s

When we investigate 6, though, it leads to contradiction. 4 tells us there are either two or three A?s, yet 6 leads us to multiple equally valid answers if that is the case, so all we know is that 1-A is wrong. Ugh.

Well, that means 2-B is wrong. Hmm, it also means 3-B must be wrong since 1-B is wrong.

So, guess 1-C. This means we have 4-B. Hmm, we can?t have 2-A, that gives too many A?s

We can also see 6-A, B or D produce immediate contradictions. That means 2-E is wrong.

This means 2 is either C or D, and there is one A and three E?s between 3,5,6,10

Since 6 can?t be A it is E. Since there is one A and six says there can?t be that many of any other, there must be another D, hence 2-D. That means 5-E.

Since there is only one A, 3 must be E, giving us 10-A.

This is a completely self-consistent answer and matches what wolfgang got. Now the questions is, what is the nifty logic I could have used to solve it easier?

Title: Re: Logic: and the answer is...
Post by wolfgang on Feb 3^rd, 2003, 6:50am

I used some of the same logic that aero_guy did, but I think I also used a lot more trial and error. And I really didn't think there was any point to typing out a whole list of all the combinations I tried that didn't work, hence just the answer.

Title: Re: Logic: and the answer is...
Post by wolfgang on Feb 3^rd, 2003, 7:32am

I got a little lucky in that one of the first purely trial and error guesses I made was that 2 was D, because that would also answer number 1, 5, and 6, and 1 would answer 4.
Considering all the possibilities in the remaining 5 questions that were also ruled out, it didn't take a huge amount of guessing to complete the puzzle. But I started with a guess and I ended with a lot of guesses, so my method doesn't teach you a whole lot.

Title: Re: Logic: and the answer is...
Post by aero_guy on Feb 5^th, 2003, 10:06pm

Yeah, it was a little silly to write it all out, but I was feeling in a silly mood. I think there was some good stuff early on, in that there were few guesses and the questions that were used were chosen for a reason but halfway through it all goes to pot. I was hoping that there was an elegant way to figure out the second half without all that guessing, but I expect there is not. I still haven't tried the other two possible guesses to see if they work out to equally viable answers. I guess 'proving' that you have the ONLY solution is the hardest part when you guess.

Title: Re: Logic: and the answer is...
Post by arkantos on Feb 6^th, 2003, 5:47pm

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccccccccccccddddddddddddddddddddddddddddddddddddddddddddddddddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeefffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffgggggggggggggggggggggggggggggggggggggggggggggggggggghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiijjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnooooooooooooooooooooooooooooooooooooooooooooooooooooppppppppppppppppppppppppppppppppppppppppppppppppppppqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz :) ;) :D ;D >:( :( :o 8) ??? ::) :P :-[ :-X :-/ :-* :'(

Title: Re: Logic: and the answer is...
Post by James Fingas on Feb 7^th, 2003, 11:29am

Arkantos >:(

No, I really don't think spam is the answer.