What day of the week was 15 August 1947?
SHORT ANSWER
Friday. Count odd days (days beyond complete weeks): 1,900 years give 1 odd day, 1901 to 1946 give 46 + 11 leap days = 57, which is 1, and 1 January to 15 August 1947 gives 227 days, which is 3. Total 5 odd days, and 5 corresponds to Friday.
Explain it simply
Any count of days can be reduced to "odd days", the remainder after removing full weeks. Known facts: 100 years have 5 odd days, 200 years 3, 300 years 1, and 400 years 0. Add the odd days up to the date, take the remainder by 7, and map 0 = Sunday, 1 = Monday, ..., 6 = Saturday.
Example
Question: Find the day for 15 August 1947.
- First 1,600 years: 0 odd days. Next 300 years (to 1900): 1 odd day.
- 1901 to 1946 = 46 years, with 11 leap years (1904 to 1944). Odd days = 46 + 11 = 57, and 57 mod 7 = 1.
- 1947 up to 15 August: Jan 31, Feb 28, Mar 31, Apr 30, May 31, Jun 30, Jul 31, Aug 15 = 227 days. 227 mod 7 = 3.
- Total = 0 + 1 + 1 + 3 = 5. Day 5 = Friday.
js
const leapsUpTo = y => Math.floor(y / 4) - Math.floor(y / 100) + Math.floor(y / 400);
const years = 1946;
const before = years + leapsUpTo(years);
const inYear = 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15;
const days = ["Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"];
console.log(inYear); // Output: 227
console.log(days[(before + inYear) % 7]); // Output: FriWhat to say in the interview
"I count odd days: 1 up to 1900, 1 more for 1901 to 1946, and 3 for the days of 1947 up to 15 August. That's 5, which maps to Friday."
Common mistakes
- Treating 1900 as a leap year; century years are leap only if divisible by 400.
- Counting the whole of August instead of 15 days.