Among one year (365 days), the number of days of “ Friday the 13th” is considered.
(1) What day of the week does the 1st day of February to December in the case of the year whose January 1st is Monday?
Write a day of the week in a table below.
(2) Find the number of days on “Friday, the 13th” which is the most in one year.
Moreover, find the number of days in the case of the fewest.
Solution
(1) It calculates what days is the 1st day of every month counts from 1st of the previous month and find a day of the week based on the remainder after being divided by 7.
February 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Tuesday is Thursday.
March 1st : 28 days, 28 / 7 = 4 remainder o.
No remainder means the day is Thursday same as February.
April 1st : 31 days, 31 / 7= 4 remainder 3.
The 3rd day from Friday is Sunday.
May 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Monday is Tuesday.
June 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Wednesday is Friday.
July 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Saturday is Sunday.
August 1: 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Monday is Wednesday.
September 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Thursday is Saturday.
October 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Sunday is Monday.
November 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Tuesday is Thursday.
December 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Friday is Saturday.
(2) The day of the week which are most in the table of (1) is Thursday.
Thursday, February 1st is shifted to Friday, February 13th.
When February 13th is set to the 1st day, March 13th is 1 + 28 = 29th day and is Friday same as Feb. 13th according to 29 / 7 = 4 remainder 1.
A day of the week shifts in the same cycle as (1) after April, too.
Therefore, three days equivalent to Thursday which are most days of the week in the table of (1).
One day equivalent to Tuesday etc. which is fewest day of the week in the table of (1).
(1) What day of the week does the 1st day of February to December in the case of the year whose January 1st is Monday?
Write a day of the week in a table below.
(2) Find the number of days on “Friday, the 13th” which is the most in one year.
Moreover, find the number of days in the case of the fewest.
Answer
(1)
(2) Most : three days, Fewest : one day
(1) It calculates what days is the 1st day of every month counts from 1st of the previous month and find a day of the week based on the remainder after being divided by 7.
February 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Tuesday is Thursday.
March 1st : 28 days, 28 / 7 = 4 remainder o.
No remainder means the day is Thursday same as February.
April 1st : 31 days, 31 / 7= 4 remainder 3.
The 3rd day from Friday is Sunday.
May 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Monday is Tuesday.
June 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Wednesday is Friday.
July 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Saturday is Sunday.
August 1: 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Monday is Wednesday.
September 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Thursday is Saturday.
October 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Sunday is Monday.
November 1st : 31 days, 31 / 7 = 4 remainder 3.
The 3rd day from Tuesday is Thursday.
December 1st : 30 days, 30 / 7 = 4 remainder 2.
The 2nd day from Friday is Saturday.
(2) The day of the week which are most in the table of (1) is Thursday.
Thursday, February 1st is shifted to Friday, February 13th.
When February 13th is set to the 1st day, March 13th is 1 + 28 = 29th day and is Friday same as Feb. 13th according to 29 / 7 = 4 remainder 1.
A day of the week shifts in the same cycle as (1) after April, too.
Therefore, three days equivalent to Thursday which are most days of the week in the table of (1).
One day equivalent to Tuesday etc. which is fewest day of the week in the table of (1).
