The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20
We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English
> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjects
Thus Dance is not a subject of Optional Category.