Elementary Number Theory and Methods of Proof Today is frid

Elementary Number Theory and Methods of Proof :

Today is friday, February 29th. What day of the week will the next Febraury 29th be?

Solution

Number of days after 29th feb to till next 29th feb

=(31+30+31+30+31+31+30+31+30+31) + 365 + 365 + 365 + (31+29)

Now take mod 7

=(3+2+3+2+3+3+2+3+2+3) + (1) + (1) + (1) + (3+1)

=33

now again take mod 7

=5

so

day on next 29th feb (5 days later on friday)

=Wednesday