RVP is a very popular multiplex in the Garden City of Bangalore. It has five screens – Screen N, Screen C, Screen W, Screen, Screen B, Screen E. Five different movies – TKR, SP, TGST, PC and EQ- were screened over five consecutive days on these screens. Each movie was shown on a different screen every day. Similarly, each screen showed a different movie every day. The following points are known

- In all screens except C, SP was screened before EQ
- TKR as third movie to be screened on screen B and it was screened after PC
- PC was screened on other two screens prior to W and was screened on N immediately after it was screened on W

Q1) Which movie was screened on the first day at screen C?

- TGST
- EQ
- PC
- Can’t be determined

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Sol:

Let’s capture the information already given in the set in a table with Screens on columns and Movies in rows. We will fill each unique row-column with sequence number based on information provided in the set.

Movies | N | C | W | B | E | Remarks |

TKR | 3 | |||||

SP | 5 | 1/2/4 | ||||

TGST | ||||||

PC | 4 | 3 | 1/2 | |||

EQ | 1 | 2/4/5 |

*In all screens except C, SP was screened before EQ*

It means, the sequence will be SP…EQ except for screen C.

Since, SP must be screened on number 5 and EQ must be displayed on number 1 on one of the screens. Let’s take SP as an example.

If SP is screened on screen N/W/B/E at 5^{th} then EQ should be on 6^{th} which is not possible.

Similarly, if EQ is screened on N/W/B/E at 1^{st} then there is no possible place of SP

Hence, we can conclude that it is Screen C only where we can adjust these two.

*TKR as third movie to be screened on screen B and it was screened after PC*

Mark TKR as 3^{rd} on screen B and give possible sequences to SP, PC, EQ

*PC was screened on other two screens prior to W and was screened on N immediately after it was screened on W*

PC is on 3^{rd} at Screen W and 4^{th} at Screen N

Now, consider PC out of 1,5,4,3 the only sequence left at that position is 2. Then complete the table with rest of the values taking references from row TKR.

Movies | N | C | W | B | E | Remarks |

TKR | 4 | 3 | ||||

SP | 5 | 2/4 | ||||

TGST | 3 | |||||

PC | 4 | 2 | 3 | 1 | 5 | |

EQ | 1 | 4/5 |

Let’s try to assign position 4 to SP other than B. We can’t give it to N, C and E (because 5 is given to PC and by rule EQ should get 5)

Case 1

Movies | N | C | W | B | E | Remarks |

TKR | 4 | 3 | ||||

SP | 5 | 4 | 2 | 4 can’t be given to N and E | ||

TGST | 3 | |||||

PC | 4 | 2 | 3 | 1 | 5 | |

EQ | 1 | 5 | 4/5 | If SP is given 4 in WàEQ at 5 |

Movies | N | C | W | B | E | Remarks |

TKR | 4 | 3 | ||||

SP | 5 | 4 | 2 | 4 can’t be given to N and E | ||

TGST | 3 | 3 | This is wrong | |||

PC | 4 | 2 | 3 | 1 | 5 | |

EQ | 1 | 5 | 4 | If SP is given 4 in WàEQ at 5 |

Hence, our assumption was wrong.

Case 2

Start with assigning 4^{th} position to SP in B and 5^{th} to EQ in B

Then TGST automatically get 2 in B

Look for places where you can assign 3 to SP so that EQ will get 4 and solve rest of the places by checking rows and columns. The final table will look like this

Movies | N | C | W | B | E | Remarks |

TKR | 1 | 4 | 5 | 3 | 2 | |

SP | 2 | 5 | 1 | 4 | 3 | Give 4 to B and 5 to EQ on B |

TGST | 5 | 3 | 4 | 2 | 1 | TGST automatically gets 2 on B |

PC | 4 | 2 | 3 | 1 | 5 | |

EQ | 3 | 1 | 2 | 5 | 4 | If SP is given 3 EQ will only get 4 in this case which is possible only at E |

Hence answer is ‘2’ (EQ was screened) [/bg_collapse]