arrengement puzzle (Question:407967.0)

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PANKAJ KUMAR KUSHWAH

· started a discussion

· 1 Months ago

arrengement puzzle (Question:407967.0)

given that there is four person betwwn T-2 seminar and six person between t1 seminar
but in solution i cant find right arrengement only these two

Question:

DIRECTIONS: These questions are based on the following information.

During the seminar week in a college, two seminars on each of the seven topics T₁, T₂, T₃, T₄, T₅, T₆ and T₇ are to be given by different professors among - P₁, P_2, P₃, P₄, P₅, P₆ and P₇. The seminars are to be arranged in seven days from Monday through Sunday. Two seminars are to be given on two different topics, in two sessions (morning and afternoon) on each day such that the seminar on each topic is to be given twice in that week. Each professor should give the seminar in two different sessions, for example if a professor gave the seminar on Monday in the morning session, he cannot give the seminar in the morning session in any of the remaining days. Each professor gives his both the seminars in the same topic. We know the following information.

(i) On any three consecutive days, any professor can give at most one seminar.

(ii) P₂ gives seminar on T₄ and P₅ is the first as well as the last professor to give the seminar.

(iii) P₇’s seminar must be arranged on Wednesday afternoon and P₃’s seminar must be arranged on Thursday morning.

(iv) The arrangement was made such that on two of the days only P₁ and P₆ give the seminar and P₁ completes the session before P₆.

(v) Between the seminars on T₂, four seminars are to be given and between the seminars on T₁, Six seminars are arranged to be given.

(vi) The seminar on T₃ is arranged to be given on Friday in morning session and the seminar on T₇ is arranged to be given on Sunday in morning session.

(vii) The seminar on T₂ cannot be on Monday but both the seminars on T₂ are to be finished before the last seminar on T₅.

On which day is the second seminar on T₆ arranged?

Options:

Thursday

Friday

Saturday

Sunday

Cannot be determined

Solution:

Ans: (a) From the given information, we have:

-	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Morning	P₅ ()	-	-	P₃ ()	(T₃)	-	(T₇)
Afternoon	-	-	P₇()	-	-	-	P₅()

From (iv), P₁, and P₆ should give the seminars on Tuesday and on either Friday or Saturday.

Also, on Tuesday P₆ should give in the morning session, so that his second seminar should be after the two seminars of P₁.

∴ P₃ has given a seminar on Monday afternoon. [from (i)]

∴ The only slots for P₂ (T₄) are Wednesday morning and Saturday afternoon.

∴ P₆ should give the second seminar on Friday afternoon.

∴ The only slots left for P₄ are Thursday afternoon and Sunday morning.

∴ The second seminars of P₇ and P₁ are to be held on Saturday and Friday mornings respectively.

From (v), the only possible slots for T₁, is Tuesday morning and Friday afternoon.

From (vii), the only slots for T₂ are Wednesday afternoon and Saturday morning.

∴ T₅ is on Sunday afternoon.

The final distribution is as follows:

-	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Morning	P₅ (T₅)	P₆(T₁)	P₂(T₄)	P₃(T₆)	P₁(T₃)	P₇(T₂)	P₄(T₇)
Afternoon	P₃(T₆)	P₁(T₃)	P₇(T₂)	P₄(T₇)	P₆(T₁)	P₂(T₄)	P₅(T₅)