# Find the order of students presentation(logical puzzle)

Four students P, Q, R and S each working under the super vision of one of the four professors A, B, C and D made their final year MBA Project Presentations one by one, one each in the areas of Finance, Marketing, Systems and Human Resource Management (HRM). Each professor is an expert in only one of the above areas and supervised exactly one of the above students in his own area. The following are the clues:

(i) First presentation was made by R.
(ii) Prof. B works in Finance.
(iii) Prof. D was P’s supervisor.
(iv) The last presentation was in the Systems area.
(v) S’s project was in the HRM area.
(vi) Prof. B’s student’s presentation followed that of Prof. C’s student.


Find:

Order of Presentation.
Each students Subjects.
Mentor of each student.

• Typically these types of 'einstein puzzles' should be written so that no assumptions/scenario's need to be tested, and specifically they should only lead to a unique result. While I enjoy the concept of these puzzles, this simply is a poor example. – Tim Couwelier Sep 6 '14 at 7:13
• Yes I know that there should be a unique solution but its not a hard and fast rule. Just to check one's ability of reaoning we can have such questions having multiple solutions so as to increase the level of difficulty. – toadalskiii Sep 6 '14 at 7:27

     1          2          3          4
---------------------------------------------
R          S          Q          P
A          C          B          D
Marketing  HRM        Finance    Systems


Edit: explanation:

question information:

B and finance are connected, so the only student that can pick both of them is Q:

so, R cannot pick Finance, also R is 1st and Systems is last therefore R cannot pick Systems as well as HRM.

Hence we can see that the only option for P is Systems:

As B is exactly after C, Here We have two possible answers:

     1          2          3          4
---------------------------------------------
R          S          Q          P
*A*       *C*        *B*         D
Marketing  HRM        Finance    Systems


OR

     1          2          3          4
---------------------------------------------
R          Q          S          P
*C*        *B*        *A*         D
Marketing  Finance    HRM        Systems

• you arr very welcome! btw, getting some up-votes is almost impossible in puzzling! – Rafe Sep 6 '14 at 10:18
• @Rafe Well, I can't let that much work go in without providing some support for it. Explanations are one thing, but visuals and explanations are worth a lot more. – Xrylite Sep 11 '14 at 23:49

N -  Prof  -  Stud  -  Area
1 - [ABCD] - [PQRS] - [FHMS]
2 - [ABCD] - [PQRS] - [FHMS]
3 - [ABCD] - [PQRS] - [FHMS]
4 - [ABCD] - [PQRS] - [FHMS]


Apply rules 1 (R first) and 4 (Systems last), they're quite straightforward.

1 - [ABCD] - [  R ] - [FHM ]
2 - [ABCD] - [PQ S] - [FHM ]
3 - [ABCD] - [PQ S] - [FHM ]
4 - [ABCD] - [PQ S] - [   S]


Since B works in finance (2), his student can't go last.

1 - [ABCD] - [  R ] - [FHM ]
2 - [ABCD] - [PQ S] - [FHM ]
3 - [ABCD] - [PQ S] - [FHM ]
4 - [A CD] - [PQ S] - [   S]


Student S is in HRM (5):

1 - [ABCD] - [  R ] - [F M ]
2 - [ABCD] - [PQ S] - [FHM ]
3 - [ABCD] - [PQ S] - [FHM ]
4 - [A CD] - [PQ  ] - [   S]


B is immediately after C (6) - B can't be first, C can't be third or fourth.

1 - [A CD] - [  R ] - [F M ]
2 - [ABCD] - [PQ S] - [FHM ]
3 - [AB D] - [PQ S] - [FHM ]
4 - [A  D] - [PQ  ] - [   S]


Remember that B is in finance, leaving 1 = R = Marketing.

1 - [A CD] - [  R ] - [  M ]
2 - [ABCD] - [PQ S] - [FH  ]
3 - [AB D] - [PQ S] - [FH  ]
4 - [A  D] - [PQ  ] - [   S]


Since D is P's professor, he can't be R's.

1 - [A C ] - [  R ] - [  M ]
2 - [ABCD] - [PQ S] - [FH  ]
3 - [AB D] - [PQ S] - [FH  ]
4 - [A  D] - [PQ  ] - [   S]


Now, let's try trial and error quickly:

Assume 1 = A

1 - [A   ] - [  R ] - [  M ]
2 - [ BCD] - [PQ S] - [FH  ]
3 - [ B D] - [PQ S] - [FH  ]
4 - [   D] - [PQ  ] - [   S]


C can then only be 2, which leaves B 3 and D 4.

1 - [A   ] - [  R ] - [  M ]
2 - [  C ] - [PQ S] - [FH  ]
3 - [ B  ] - [PQ S] - [FH  ]
4 - [   D] - [PQ  ] - [   S]


D is with P; B works in Finance; S is in HRM.

Solution 1

   1 - [A   ] - [  R ] - [  M ]
2 - [  C ] - [   S] - [ H  ]
3 - [ B  ] - [ Q  ] - [F   ]
4 - [   D] - [P   ] - [   S]


Aha, a solution!

Now, let's see if 1 = C works:

Assume 1 = C

1 - [  C ] - [  R ] - [  M ]
2 - [AB D] - [PQ S] - [FH  ]
3 - [AB D] - [PQ S] - [FH  ]
4 - [A  D] - [PQ  ] - [   S]


B is immediately after. Remember he's in finance.

1 - [  C ] - [  R ] - [  M ]
2 - [ B  ] - [PQ S] - [F   ]
3 - [A  D] - [PQ S] - [ H  ]
4 - [A  D] - [PQ  ] - [   S]


S is in HRM

1 - [  C ] - [  R ] - [  M ]
2 - [ B  ] - [ Q  ] - [F   ]
3 - [A  D] - [   S] - [ H  ]
4 - [A  D] - [PQ  ] - [   S]


D is with P

Solution 2

   1 - [  C ] - [  R ] - [  M ]
2 - [ B  ] - [ Q  ] - [F   ]
3 - [A   ] - [   S] - [ H  ]
4 - [   D] - [P   ] - [   S]


Well, that's another solution fully consistent with the rules. Turns out this puzzle has two correct answers.