Question

Show that days with the identical calendar date in the years 1999 and 1915 fell on the same day of the week.

Answer 1

http://gyazo.com/7b69acf92895f6f87e047c6f7955c037

Answer 2

whats so special about 1999 :O or 1915

Answer 3

http://prntscr.com/58jsot

Answer 4

so basically we need to avoid one years each 4 years and count more 7 to get a year with same identical calendar date ... that would be each two 11 years and one 6 years

Answer 5

so,
1999-1915=0 mod 7 xD

Answer 6

bhahaha xD

Answer 7

this is nice to show what day next year would be

Answer 8

I see... if you have time could you help me with solution

Answer 9

solution for what :O

Answer 10

i mean proof

Answer 11

like proper proof ?

ok , main i dea is to show that 1999-1915 =0 mod 7

Answer 12

\[Y_1 \equiv Y2 \pmod {7}\] doesnt necessarily mean they will have exact same "day name" on each day of the entire year rigt ?

Answer 13

If thats the case we will be having that pattern every 7 years i guess

Answer 14

nope , count 7+4=11
when we have leap in the start
and 7-1 when we dont have

Answer 15

thats for advancing a year ?

Answer 16

?