Simple way to calculate the day for any date
17th January 2018
Disclaimer : I found this method on YouTube; I merely wrote it down for convenience (so I can make a program someday) and thought I should share it with you all.
Here’s the source : Video Link
Prerequisites

Let Sunday = 0, Monday = 1 …. Saturday = 6

Doomsdays 
The day shared by specific dates (day changes by year, dates remain same)
Jan/3(4th in Leap), Feb/28th (29th in leap), Mar/14th, Apr/4th … can be written as
1/3(4), 2/28(29), 3/14, 4/4, 5/9, 6/6, 7/11, 8/8, 9/5, 10/10, 11/7, 12/12
For even months, it’s same date as the month (expect Feb) For Feb it’s the last day (29 or 28 depending on leap or not) For odd months : working 9/5 on 7/11 (reverse holds true), Pie 3/14, Jan is 3rd or 4th (Leap)
Eg : 2018’s doomsdays are all Wednesdays

Century Code 
In gregorian calendar, dates repeat every 400 years. so only 4 century codes possible/required
… 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 …
3(Wed) 2(Tue) 0(Sun) 5(Fri)
Eg : 2000’s doomsday = Tuesday => 2000’s code = 2
Algorithm
Input = dd/mm/yyyy
 Century Code = I (from Prerequisite no 3)
 00yy/12 = Quotient (M) + Remainder (R)
 R/4 = Quotient (L) + Remainder
 I + M + R + L = X
 X/7 = Quotient + Remainder (D) (from Prerequisite no 1)
 Y = date of doomsday for given mm (from Prerequisite no 2)

dd  Y / 7 = Quotient + Remainder (T)  (D + T) / 7 = Quotient + Remainder (Output/Answer)
Notes
> Variable assignment : Quotient (A) + Remainder (B) means A = Quotient and B = Remainder
> These variables represent fingers on the hand (for manual calculations) : I = Index, M = Middle, R = Ring, L = Little, T = Thumb
> All calculations involve whole numbers only
> D stands for Doomsday; so named by the inventor of this method John H Conway
> For more (visual) explanation, please refer to the video
Examples
Eg 1 : Day on 6th Dec 2030
 I = 2
 30/12 = 2 + 5 => M = 2, R = 6
 6/4 = 1 + 2 => P = 1
 2 + 2 + 6 + 1 = 11 => X = 11
 11/7 = 1 + 4 => D = 4 (Thursday)
 Y = 12 (From mm = 12)

16  12 / 7 = 0 + 4 => T = 4  (4 + 4) / 7 = 1 + 1 => Ans = 1 = Monday
Eg 2 : Day on 23rd Sept 1105
 I = 3
 5/12 = 0 + 5 => M = 0, R = 5
 5/4 = 1 + 1 => P = 1
 3 + 0 + 5 + 1 = 9 => X = 9
 9/7 = 1 + 2 => D = 2 (Tue)
 Y = 5

23  5 / 7 = 1 + 4 => T = 4  (2 + 4) / 7 = 0 + 6 => Ans = 6 = Saturday