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Examples 6 to 8

(6) Prove that any date in March of a year is the same day of the week as the corresponding date in November that year.

Soln. Since, the no. of odd days between 1^st March to 1^st November is 0 ( $\because$ 21 days ).

$\therefore$ Any date in March of a year is the same day of the week as the corresponding date in November that year.

The first day of any century is either Monday or Tuesday or Thursday or Saturday.

( For it keep in mind : 1246 )

The last day of any century is either Sunday or Monday or Wednesday or Friday.

( For it keep in mind : 0135 )

(7) If the day on 15^th August, 1947 was Friday, then find the day on 15^th August, 1957.

Soln. The no. of odd days between 15^th August,1947 to 15^th August, 1957 is 6

( 10 + 3 = 13 days ).

Friday

+ 6 Odd day
Thursday

$\therefore$ The day on 15^th August, 1957 was Thursday.

(8) If the day on 16^th July, 1776 was Thursday, then find the day on 16^th July, 1765.

Soln. The no. of odd days between 16^th July, 1776 to 16^th July, 1765 is 0

( $\because$ 11 + 3 = 14 days ).

Thursday

– 0 Odd day
Thursday

$\therefore$ The day on 16^th July, 1765 was Thursday.