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Here 1600 years have ‘0’ odd day .......(A).

100years have ‘5’ odd days ..........(B)

75years = (18leap years + 57ordinary years)

= (18 × 2 + 57 × 1)

= 93odd days

= (7 × 13 + 2) = ‘2’ odd days ........(C)

Now, the no. of days from 1st January to 18 July, 1776

= 182 + 18 = 200days

= (28 × 7 + 4)days = ‘4’odd days ...... (D)

Adding (A) + (B) + (C) + (D),

We get, 0 + 5 + 2 + 4 = 04odd days

Ans. Thursday

For determining the dates, we find the days on 1^st Oct, 1975.

1600years have ‘0’ odd days ............(A).

300years have ‘01’ odd days ..........(B)

74years have (18 leap years + 56 ordinary years)

2 × 18 + 1 × 56 = 92 odd days

= ‘01’ odd days ......(C)

Days from 1^st January to 1^st Oct., 1975

1^st Jan - 30 June + 1^st July to 1st Oct.

181 + 31 + 31 + 30 + 1 = 274days

= ‘01 odd days ....(D) (274/7 = 01days)

Adding (A) + (B) + (C) + (D) = 0 + 01 + 01 + 01 = ‘03’ odd days

Ans. Wednesday (1^st Oct), hence, 7, 14, 21, 28, Oct. will Tuesday fall

1996 1997 1998 1999 2000 2001 2002 2003

2 1 1 1 2

Total = 2 + 1 + 1 + 1 + 2 = 7 = 0 odd days

Hence, year 2001 will have the same calendar as year 1996.

Sol. 100years have = 5 odd days ∴ Last days of Ist century is Friday 

200years have = 10 odd days ∴ Last day of IIst century is Wednesday 

= 3 odd days 

300years have = 15 odd days ∴ Last day of IIIrd century is Monday 

= 01 odd day 

400years have = (5 × 4 + 1) Last day of 4th century is Sunday 

= 21 odd days 

= 0 odd days 

Since the order keeps on cycling, we see that the lat day of the century cannot be Tuesday, Thursday or Saturday.