Question

Find the day of the week on 26 January 1950?

Answer 1

Hint: Here in this question, we have to determine the day of the week 26 January 1950. We have a code for the days, months and years. So by using these codes, we have a formula and that is given by \[\dfrac{{(Date + Month\,\,code + \,No.\,of\,years + No.\,\,of\,leap\,years + \,year\,code)}}{7}\]. When we divide the number by 7, the remainder value will represent the day of the week 26 January 1950.

Complete answer:
To solve this kind of problem we have to know about the code.
Day code:
Saturday = 0, Sunday = 1, Monday = 2, Tuesday = 3, Wednesday = 4, Thursday = 5 and Friday = 6.
Month codes:
January = 1, February = 4, March = 4, April = 0, May = 2, June = 5, July = 0, August = 3, September = 6, October = 1, November = 4 and December = 6.
Century code:
\[\begin{array}{*{20}{l}}
  {1500{\text{ }} - {\text{ }}1599{\text{ }} = {\text{ }}0} \\
  {1600{\text{ }} - {\text{ }}1699{\text{ }} = {\text{ }}6} \\
  {1700{\text{ }}-{\text{ }}1799{\text{ }} = {\text{ }}4} \\
  {1800{\text{ }}-{\text{ }}1899{\text{ }} = {\text{ }}2} \\
  {1900{\text{ }}-{\text{ }}1999{\text{ }} = {\text{ }}0} \\
  {2000{\text{ }}-{\text{ }}2099{\text{ }} = {\text{ }}6} \\
  {2100{\text{ }}-{\text{ }}2199{\text{ }} = {\text{ }}4} \\
  {2200{\text{ }}-{\text{ }}2299{\text{ }} = {\text{ }}2} \\
  {2300{\text{ }}-{\text{ }}2399{\text{ }} = {\text{ }}0}
\end{array}\]
To determine the day we have the formula, and it is given by
\[\dfrac{{(Date + Month\,\,code + \,No.\,of\,years + No.\,\,of\,leap\,years + \,year\,code)}}{7}\]
Here the date is 26, The month code is 1, the number of years from 1900 to 1950 is 50.
In the 50 years we have 12 leap years. The year code is 0.
Substituting all these values we have
\[ \Rightarrow \dfrac{{(26 + 1 + \,50 + 12 + \,0)}}{7}\]
On adding all the terms in the numerator, we have
\[ \Rightarrow \dfrac{{89}}{7}\]
Now on dividing the number 89 by 7 we get the remainder as 5. Here the remainder value will represent the day code.
The 5 will represent the day Thursday.
Therefore, the day of the week on 26 January 1950 is Thursday.

Note:
We have century codes for every 100 years. The given year will be present in the given century. So how many years will be completed from the starting year to the given year in the century period where the given year will be present, that is the number of years in the formula. The number of leap years will be determined by the number of years.