8
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Question:

Eight people are sitting in two parallel rows containing four people each, in such a way that there is a equal distance between and adjacent persons. In row 1 , A,B,C,D are seated and all of them are facing south . In row 2 , E,F,G,H are seated and all of them are facing North. Therefore , in the given sitting arrangement each member seated in a row faces another member of other row. Each one them also have different profession, viz. Engineer, Doctor, Teacher, Pilot, Businessman , Banker , Lawyer and Builder but not necessarily in the same order.

B sits in second to the right of the builder. G faces the immediate neighbor of the Builder. Only one person sits between G and the pilot. Two people sit between H and the Lawyer. D faces the immediate neighbor of pilot.Only one person sits between teacher and C . Teacher does not sit at any of the extreme ends. Immediate neighbor of D faces the doctor, E faces engineer, F is not a banker.

  1. Who among the following sit in the extreme ends of the rows ?

a) B and pilot,
b) C and builder
c) The Builder and G
d) G and the engineer
e) A,G

  1. Who among the following is the banker ?

a) A
b) B
c) C
d) E
e) G

  1. Who is/are seated between lawyer and the doctor ?

a) Pilot only
b) G and the businessman
c) F,E
d) businessman and the banker
e) No one

  1. Who among the following faces the businessman ?

a) A
b) Doctor
c) F
d) Teacher
e) Builder

  1. Which of the following is true regarding G ?

a) D faces G
b) The pilot is an immediate neighbor of G
c) G faces the person who is second left to the Banker
d) G is the doctor
e) G sits at one of the extreme ends of the line.

End of question

I got this arrangement (along with many others while trying to solve them) but I always get stuck with contradictory situations. (and I know it must be wrong).

(B),(),(D),(C)
(Lawyer),(Builder, G), (Doctor),(Pilot E)

I am practicing logic-puzzle questions and of many types , I can't solve this type of problem when ever I come across them. I know once if I could solve even one of them I would learn to solve the others. (I know stack-exchange communities are normally very strict regarding the type of questions posted, hope this fits into it. I tried a lot of times but I can't solve this one and need help and also please explain how did you got the answer)

Thanks for any help.

Answers:
1) a)
2) c)
3) e)
4) e)
5) d)

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  • $\begingroup$ Dosen't A face E,B face F,C face G,D face H? $\endgroup$ – Spikatrix Jan 26 '15 at 12:16
  • $\begingroup$ It is not necessary they are in the same order, but first row faces the second row and vice versa $\endgroup$ – keyboard-k Jan 26 '15 at 12:35
  • $\begingroup$ Ok. Suppose A and D are at the rightmost and leftmost ends of the row. Is D the neighbour of A? Also does A sit to the left of D? $\endgroup$ – Spikatrix Jan 26 '15 at 12:38
  • $\begingroup$ No, "neighbour" means they should be right beside them, as in front (in same row) in back (in same row) or in side (in the opposite row) $\endgroup$ – keyboard-k Jan 26 '15 at 12:53
  • 1
    $\begingroup$ Are you sure the question is right? I can't seem to find a proper solution. Also , suppose A sits in the 2nd position from the right in the first row and D in the 1st position from the left in the first row. Is D 2 places right of A? $\endgroup$ – Spikatrix Jan 26 '15 at 13:33
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New Edit, now that question has been corrected. Apologies if this is over-long, but you did ask for explanation at how to arrive at the answer.

I'll work through it long-hand, because the worse case is only 3 possibility trees, and they soon collapse under contradiction. So here goes:

B sits in second to the right of the builder

This gives two possible options. Branch 1:

X   X   Bui X
B   X   X   X

X   X   X   X
X   X   X   X

Or Branch 2:

X   X   X   Bui
X   B   X   X

X   X   X   X
X   X   X   X

G faces the immediate neighbor of the Builder

Taking branch 1 as the start point, we end up with two possibilities. Branch 1.1:

X   X   Bui X
B   X   X   X

X   X   X   X
X   G   X   X

Branch 1.2:

X   X   Bui X
B   X   X   X

X   X   X   X
X   X   X   G

But from branch 2 there is only one possibility:

Branch 2:

X   X   X   Bui
X   B   X   X

X   X   X   X
X   X   G   X

Only one person sits between G and the pilot

For each of our 3 possible branches there is just one solution that matches this, so our branches now look like this:

Branch 1.1:

X   X   Bui X
B   X   X   X

X   X   X   Pil
X   G   X   X

Branch 1.2:

X   X   Bui X
B   X   X   X

X   Pil X   X
X   X   X   G

Branch 2:

X   X   X   Bui
X   B   X   X

Pil X   X   X
X   X   G   X

Two people sit between H and the Lawyer

Again each of our branches only has one option that matches this.

Branch 1.1:

X   X   Bui X
B   X   X   X

Law X   X   Pil
X   G   X   H

Branch 1.2:

X   X   Bui X
B   X   X   X

X   Pil X   Law
H   X   X   G

Branch 2:

X   X   X   Bui
X   B   X   X

Pil X   X   Law
H   X   G   X

D faces the immediate neighbor of pilot

This is good, as there is no way to satisfy branch 2 with this condition. There is just one possible solution for each of our other branches.

Branch 1.1:

X   X   Bui X
B   X   D   X

Law X   X   Pil
X   G   X   H

Branch 1.2:

X   X   Bui X
B   X   D   X

X   Pil X   Law
H   X   X   G

Only one person sits between teacher and C . Teacher does not sit at any of the extreme ends

Taking both of these together saves a step, because it reduces the possible seats of the teacher to the middle two seats. For both of our branches there is only one possible solution.

Branch 1.1:

X   Tea Bui X
B   X   D   C

Law X   X   Pil
X   G   X   H

Branch 1.2:

X   Tea Bui X
B   X   D   C

X   Pil X   Law
H   X   X   G

Immediate neighbor of D faces the doctor

This condition gets rid of branch 1.2, because we know the neighbour of D in that branch must face the pilot or the lawyer. Branch 1.1 has only one possible solution:

X   Tea Bui X
B   X   D   C

Law Dr  X   Pil
X   G   X   H

E faces engineer

E must be on the bottom row, and the only unknown letter that faces an unknown occupation gives a single solution:

Eng Tea Bui X
B   X   D   C

Law Dr  X   Pil
E   G   X   H

F is not a banker

This condition allows us to finish the puzzle. F is on the bottom row, and the only remaining unknown occupation is the business man. This allows us to fill in the remaining X's.

Eng Tea Bui Ban
B   A   D   C

Law Dr  Bus Pil
E   G   F   H

Which allows us to answer the questions as:

1) A

2) C

3) E

4) E

5) D

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I apologize for this answer being so long. I tried to note all of my logic as I worked through the puzzle myself, only to find that (I think) it is impossible as typed. I believe there is a typo in one of the clues. ("Only two person sits between..." I believe should be "Only one person sits between...") For the sake of logic-checking, I maintained my first work with the typo, then put all of the work for the fixed version after the line break. My answers to the questions are:

A, C, E, ??, D

My work:

(A - H will be used as above. Occupations will be abbreviated as EN, DO, TE, PI, BS, BA, LA and BL. A single seat is represented first by the letter, then by the occupation, or -/--.)

B sits in second to the right of the builder

This means that there is exactly one seat between B and the builder, and that B will be to the builder's right-hand side, which changes their orientation depending on the row in which they sit. This gives us four possible positions. I think rotation is arbitrary, however, so that gives us two possibilities. (Incidentally, this also means that B is not the Builder.)

-/--, -/--, -/--, -/--
-/BL, -/--, B/--, -/--

-/--, -/--, -/--, -/--
-/--, -/BL, -/--, B/--

G faces the immediate neighbor of the Builder.

This means that Builder's neighbor, x, sits next to Builder, and across from G. This positions G diagonal from Builder. There are only three possible positions for G. (This also means G isn't Builder.)

-/--, G/--, -/--, -/--
-/BL, -/--, B/--, -/--

G/--, -/--, -/--, -/--
-/--, -/BL, -/--, B/--

-/--, -/--, G/--, -/--
-/--, -/BL, -/--, B/--

Only two person sits between G and the pilot.

I question whether this one should say "only one person sits between..." If so, that changes everything from here on.

Well, this means there are two empty seats between G and Pilot. There is only one situation in which this is possible, our second layout above. (This also eliminates G as Pilot, and B as Pilot, since there is no scenario in which G and B are two seats apart.)

G/--, -/--, -/--, -/PI
-/--, -/BL, -/--, B/--

Two people sit between H and the Lawyer.

This tells us that H is on one end of a row while Lawyer is on the other. Unfortunately, there are many scenarios in which this can be true. So I'm going to ignore it for now and see if it's more significant on my second loop through the clues.

D faces the immediate neighbor of pilot.

We know where Pilot is sitting, and he only has one neighbor. So we can easily conclude that D sits next to B in our layout.

G/--, -/--, -/--, -/PI
-/--, -/BL, D/--, B/--

Only one person sits between teacher and C.

This gives us a lot of options. If you combine it with the next clue, however, it narrows it down quite a bit.

Teacher does not sit at any of the extreme ends.

This means Teacher must sit in one of the four middle seats. But since the previous clue says C is one spot away from Teacher, there are two places where Teacher can't be sitting because B and G are already occupying the place where C would have to sit in those cases. So now we have:

G/--, -/TE, -/--, C/PI
-/--, -/BL, D/--, B/--

G/--, -/--, -/--, -/PI
C/--, -/BL, D/TE, B/--

Immediate neighbor of D faces the doctor.

D's immediate neighbors are B and Builder. Since we know that B is already facing the Pilot, that means Builder must be facing the Doctor. This eliminates our first layout above, since Teacher is positioned across from Builder there.

G/--, -/DO, -/--, -/PI
C/--, -/BL, D/TE, B/--

E faces engineer, F is not a banker.

These two clues don't seem to help much right now, since we haven't dealt with E, F, Engineer or Banker thus far. I'd like to revisit the clue I skipped earlier, though.

Two people sit between H and the Lawyer.

This clue means that H and Lawyer are at opposite ends of the same row. There is only one possible place where H could be positioned at the end of a row now.

G/LA, -/DO, -/--, H/PI
C/--, -/BL, D/TE, B/--

Aaaaand this makes E faces Engineer impossible. So I'm guessing that the third clue was probably typed wrong. Or maybe I messed up somewhere. Let me back up and try it the other way...


B sits in second to the right of the builder

This means that there is exactly one seat between B and the builder, and that B will be to the builder's right-hand side, which changes their orientation depending on the row in which they sit. This gives us four possible positions. I think rotation is arbitrary, however, so that gives us two possibilities. (Incidentally, this also means that B is not the Builder.)

-/--, -/--, -/--, -/--
-/BL, -/--, B/--, -/--

-/--, -/--, -/--, -/--
-/--, -/BL, -/--, B/--

G faces the immediate neighbor of the Builder.

This means that Builder's neighbor, x, sits next to Builder, and across from G. This positions G diagonal from Builder. There are only three possible positions for G. (This also means G isn't Builder.)

-/--, G/--, -/--, -/--
-/BL, -/--, B/--, -/--

G/--, -/--, -/--, -/--
-/--, -/BL, -/--, B/--

-/--, -/--, G/--, -/--
-/--, -/BL, -/--, B/--

Only ONE person sits between G and the pilot.

This gives Pilot three possible positions:

-/--, G/--, -/--, -/PI
-/BL, -/--, B/--, -/--

G/--, -/--, -/PI, -/--
-/--, -/BL, -/--, B/--

-/PI, -/--, G/--, -/--
-/--, -/BL, -/--, B/--

D faces the immediate neighbor of pilot.

This positions D diagonally from Pilot, which puts him in only two possible positions:

G/--, -/--, -/PI, -/--
-/--, D/BL, -/--, B/--

-/PI, -/--, G/--, -/--
-/--, D/BL, -/--, B/--

Only one person sits between teacher and C. Teacher does not sit at any of the extreme ends.

This puts us at five possibilities. Not fun.

G/--, -/TE, -/PI, C/--
-/--, D/BL, -/--, B/--

G/--, -/--, -/PI, -/--
C/--, D/BL, -/TE, B/--

C/PI, -/--, G/TE, -/--
-/--, D/BL, -/--, B/--

-/PI, -/TE, G/--, C/--
-/--, D/BL, -/--, B/--

-/PI, -/--, G/--, -/--
C/--, D/BL, -/TE, B/--

Immediate neighbor of D faces the doctor.

This at least eliminates the middle option, since both diagonals from D already have an occupation.

G/--, -/TE, -/PI, C/--
-/--, D/BL, -/--, B/--

G/--, -/--, -/PI, -/--
C/--, D/BL, -/TE, B/--

-/PI, -/TE, G/--, C/--
-/--, D/BL, -/--, B/--

-/PI, -/--, G/--, -/--
C/--, D/BL, -/TE, B/--

Two people sit between H and the Lawyer.

There are many possibilities for this, but I'm hoping other clues will narrow them down...

G/--, -/TE, -/PI, C/--
H/--, D/BL, -/--, B/LA

G/LA, -/--, -/PI, H/--
C/--, D/BL, -/TE, B/--

H/PI, -/TE, G/--, C/LA
-/--, D/BL, -/--, B/--

-/PI, -/TE, G/--, C/--
H/--, D/BL, -/--, B/LA

H/PI, -/--, G/--, -/LA
C/--, D/BL, -/TE, B/--

E faces engineer.

This actually does narrow it down a little:

G/--, -/TE, E/PI, C/--
H/--, D/BL, -/EN, B/LA

H/PI, -/TE, G/EN, C/LA
-/--, D/BL, E/--, B/--

E/PI, -/TE, G/--, C/--
H/EN, D/BL, -/--, B/LA

-/PI, -/TE, G/EN, C/--
H/--, D/BL, E/--, B/LA

H/PI, -/--, G/EN, -/LA
C/--, D/BL, E/TE, B/--

H/PI, -/--, G/--, E/LA
C/--, D/BL, -/TE, B/EN

Immediate neighbor of D faces the doctor.

This eliminates any layouts above in which both of D's diagonals already have occupations.

G/DO, -/TE, E/PI, C/--
H/--, D/BL, -/EN, B/LA

E/PI, -/TE, G/DO, C/--
H/EN, D/BL, -/--, B/LA

H/PI, -/--, G/DO, E/LA
C/--, D/BL, -/TE, B/EN

We have no information, really, about F, A, Businessman, or Banker. But let's check out the questions and see if we have enough information to answer them.

1. Who among the following sit in the extreme ends of the rows ?

a) B and pilot

b) C and builder //This is never true in any layout.

c) The Builder and G //This is never true in any layout.

d) G and the engineer //This is never true in any layout.

e) A,G //This is never true in any layout.

**This eliminates one of our layouts above...

E/PI, -/TE, G/DO, C/--
H/EN, D/BL, -/--, B/LA

H/PI, -/--, G/DO, E/LA
C/--, D/BL, -/TE, B/EN

2. Who among the following is the banker?

a) A

b) B //This is never true in any layout.

c) C

d) E //This is never true in any layout.

e) G //This is never true in any layout.

**We can't answer this yet, but maybe we can later.

3. Who is/are seated between lawyer and the doctor ?

a) Pilot only

b) G and the businessman

c) F,E

d) businessman and the banker

e) No one //This is true in both layouts.

4. Who among the following faces the businessman ?

a) A //See note.

b) Doctor

c) F //See note.

d) Teacher //See note.

e) Builder

The Businessman must occupy a space with a blank occupation. Those blanks are never situated across from A, F, or Teacher. This also means:

E/PI, -/TE, G/DO, C/--
H/EN, D/BL, -/BS, B/LA

H/PI, -/BS, G/DO, E/LA
C/--, D/BL, -/TE, B/EN

5. Which of the following is true regarding G ?

a) D faces G //This is never true in any layout.

b) The pilot is an immediate neighbor of G //This is never true in any layout.

c) G faces the person who is second left to the Banker //This is never true in any layout.

d) G is the doctor

e) G sits at one of the extreme ends of the line. //This is never true in any layout.

2. Who among the following is the banker ?

a) A //This can't be true in either layout.

c) C

E/PI, -/TE, G/DO, C/BA
H/EN, D/BL, -/BS, B/LA

H/PI, -/BS, G/DO, E/LA
C/BA, D/BL, -/TE, B/EN

Aaand I'm stumped for the last question.

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  • $\begingroup$ +1 for spotting a scenario where this makes sense! Incidentally: Only two person sits between G and the pilot and Two people sit between H and the Lawyer tell us a lot because both of these clauses must happen on the same (bottom) row (A-D top row, E-H bottom) which means H=pilot and G=Lawyer. BUT I reckon you are correct that this was a mistake in the question. $\endgroup$ – Mashton Jan 26 '15 at 13:52
  • $\begingroup$ answers match match with the answer sheet of question paper, you were correct about the "only one person sits between.." , thanks for teaching me how to solve , should I edit the question as well ? $\endgroup$ – keyboard-k Jan 26 '15 at 15:19
  • $\begingroup$ @akiba Probably so. I still don't know how to determine where A and F are. $\endgroup$ – EFrog Jan 26 '15 at 15:21
  • $\begingroup$ @Efrog yeah.. I am trying to solve by your method. $\endgroup$ – keyboard-k Jan 26 '15 at 15:48
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First of all, the term "immediate neighbor" is misleading, because in order for this to work, it really should be "an immediate neighbor". Further, "to the right" is also misleading, because they should inform us that we are facing North.

First of all, I quickly realized this would be very difficult to solve in a completely straightforward fashion (e.g. eliminating possibilities until the answer remains), so I decided to make assumptions and which would either work out, or result in a contradiction and I could start again. Also, the possibility occurred to me - because the answers were multiple choice, it didn't ask for a complete grid - that the solution may not be unique, so making assumptions is not necessarily a bad thing.

The first thing I noticed is that there is a lot of information in the South row about people sitting far from each other, i.e.

  • Only one person sits between G and the pilot.
  • Two people sit between H and the Lawyer.

Therefore, either G must be the lawyer, or H must be the pilot. I began with the assumption:

  1. H is the Pilot.

I also made a second assumption:

  1. H is on the left (and the Lawyer is on the right).

So we have, immediately:

xxx    xxx    xxx   xxx
        D

Pil    xxx    xxx   Law
 H             G

Since the neighbor of D faces the Doctor, G must be the Doctor. Further, since G faces the immediate neighbor of the Builder, and B must be second to the right of the Builder, D must be the builder.

xxx    Bui    xxx   xxx
        D            B

Pil    xxx    Doc   Law
 H             G

Since E faces the Engineer, and D is the Builder, B must be the engineer. Further, Teacher and C are in the same row, and Teacher is not on the extreme ends, so Teacher must be on the third seat, and therefore C is the first seat. Via process of elimination, Now we have:

xxx    Bui    Tea   Eng
 C      D      A     B

Pil    xxx    Doc   Law
 H      F      G     E

Since F is not a Banker, F must be a businessman, So C is the Banker.

Ban    Bui    Tea   Eng
 C      D      A     B

Pil    Bus    Doc   Law
 H      F      G     E

A quick check of all the facts shows that this fits, and this gives the answers to the multiple choice provided by OP.

Exercise for the reader:

  1. Show that assumption 1 results in a contradiction (hint: who do the immediate neighbors of D face?)
  2. Show that assumption 2 results in a contradiction (hint: B and D can't both be two to the right of the Builder)
  3. Why do the answers to 1 and 2 show the answer is, in fact, unique?
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  • $\begingroup$ This does help a lot, but as we have limited time in answering the question (2 mins per question at max), I can't afford to be wrong as it will cost me more time. $\endgroup$ – keyboard-k Jan 27 '15 at 17:33
  • $\begingroup$ @akiba Per question or per section? I solved all 5 questions this way in less much than 10 minutes using a pen and one sheet of paper (so I couldn't even erase). Being willing to assume-and-check can help you make forward progress when trying to be super careful and deductive can take far longer. $\endgroup$ – durron597 Jan 27 '15 at 17:39
  • $\begingroup$ per section* sorry for any misunderstanding [a question has around 5 multiple choice questions] but I get your point , assumption questions are of different type in my studies. (voted +1) $\endgroup$ – keyboard-k Jan 27 '15 at 17:44
1
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Edit: OP edited a word in the question which made this answer incorrect. Here is the incorrect answer anyway:

The given situation is impossible to get.

Consider seats(from left) in first row as 1,2,3,4 and seats(from left) in second row as 5,6,7,8.

Only two(OP changed this to one) person sits between G and the pilot. Two people sit between H and the Lawyer.

This means that G,the lawyer and H,the pilot sit at the ends of the second row. So, let us assume that H sits in seat 5 and G sits in seat 8.

D faces the immediate neighbor of pilot

Would mean that D sits in seat 2.

G faces the immediate neighbor of the Builder

Would mean that Builder sits on seat 3.

B sits in second to the right of the builder

Would mean that B sits on seat 1.

Only one person sits between teacher and C . Teacher does not sit at any of the extreme ends

Would mean that Teacher ,D sits on seat 2 and C is on seat 4. This leaves A,the builder on seat 3.

So,we have

B,D,A,C (A is the builder and D is the teacher)
H,?,?,G (H is the pilot and G is the lawyer)

And

E faces engineer

is not possible.

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  • $\begingroup$ Exactly the situation I was in. Something isn't right with the question. $\endgroup$ – Mashton Jan 26 '15 at 14:21
  • $\begingroup$ It's only one person between G and the pilot... $\endgroup$ – durron597 Jan 26 '15 at 17:05
  • $\begingroup$ @durron597 it is now! When the question was posed there were two people, hence the number of answers saying it is impossible. $\endgroup$ – Mashton Jan 26 '15 at 19:03
  • $\begingroup$ @Mashton If you fix your answer I'll remove my downvote. In the mean time, my answer is correct... $\endgroup$ – durron597 Jan 26 '15 at 19:08
  • $\begingroup$ I didn't say your answer wasn't correct, just that the 3 answers here saying "this isn't possible, are you sure the question is correct?" were all given when the question was incorrect. $\endgroup$ – Mashton Jan 26 '15 at 19:10

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