Fifteenth August, 1947 was a Friday. Determine the day of the week on the Twenty-Sixth of January, 1957 ?

First, we will count odd days from 15 Aug 1947 to 26 Jan 1957

(A) From 15 Aug 1947 to 15 Aug 1956 → 9 years

Leap years in between: 1948, 1952, 1956 → 3 leap years

• Normal years = 6 → 6 × 1 = 6 odd days

• Leap years = 3 → 3 × 2 = 6 odd days

Total = 6 + 6 = 12 odd days → 12 ≡ 5 (mod 7)

Now, (B) From 15 Aug 1956 to 26 Jan 1957

Aug (remaining 16 days)
Sep = 30
Oct = 31
Nov = 30
Dec = 31
Jan = 26

Total: 16 + 30 + 31 + 30 + 31 + 26 = 164 days

164mod7 = 3 odd days

Total odd days: 5 + 3 = 8 ≡ 1 (mod 7)

Hence, the final day: Friday + 1 = Saturday