Give me a date
Anil Kumar Patnaik
Abhas entered the classroom. The children immediately stood up and wished him. Prakriti came forward and offered him chocolates from a box.
“Today is your birthday?” asked Abhas.
“No sir, this is for securing the first position in spin a yarn competition. My birthday is 1st April sir, 01 April 2004,” said Prakriti and returned to her seat.
“So, you were born on a Thursday?” asked Abhas.
“Yes sir, but how did you get that?” asked Prakriti. Even the other students gaped at Abhas sir.
“This is a simple calculation; you only have to know a few pieces of information,” he replied.
“Sir, my sister was born on 13 October 2010, can you tell us what day it was?” quizzed Prakriti. The entire class was silent, everyone was waiting for the reply.
In a minute or so Abhas replied, “Wednesday.”
“Is he right?” some children asked Prakriti.
“Yes, it was a Wednesday,” Prakriti replied astonished.
“Sir, please tell us how you do this,” everybody requested.
“Okay, I will, but then to complete today’s lesson I will take an extra class another day. Will you be fine with that?”
“Yes sir…” came the quick reply, as all students closed their textbooks.
“Okay, this calculation is done with the number 7, because our days repeat every seven days. Like every month 1,8,15,22,29 are the same day, also [2,9,16,23,30], [3,10,17,24,31{if exists}], [7,14,21,28] are same days. This is because the difference between any two numbers in each of these groups is divisible by 7.”
“Okay, today is 5th and a Wednesday, therefore 12,19, and 26 are also Wednesdays,” declared Elen.
“Yes, you are right. You know that every fourth year is a leap year and the other three years are regular. Every year, April and July, March and November, September and December have the same calendar, irrespective of whether it’s a leap year or not,” explained Abhas.
“True sir, last year both April 19 and July 19 were Fridays. I remember as the dates are my parents’ birthdays,” said Sambit.
“Correct, ordinary years and leap years have more such coincidences. You know that every fourth year is a leap year. But every 100th, 200th, and 300th years are not. This is related to the earth’s revolution around the sun and it’s a different calculation, which I will talk about later. Coming back to the topic – in 100 years, there are 76 ordinary years and 24 leap years.”
“Now have a look, in one year – 365 days means (364+1) (keeping the divisibility by 7 factor in mind) days = (52×7+1) that is equal to 52 weeks and 1 day. Which means one ordinary year has only one extra day. Similarly, in a leap year, 366 days means 52 weeks + 2days, a leap year has 2 extra days.
• 100 years = 76 ordinary years + 24 leap years
= (76×1) extra days + (24×2) extra days
= (76+48) extra days = 124 extra days,
which means (17×7 + 5) extra days
= 17 weeks + 5 extra days.
Which means 100 years have 5 extra days. – [I],
• 200 years = 10 extra days or 1 week + 3 days
= 3 extra days. – [II],
• 300 years = 15 extra days or 2 weeks + 1 day
= 1 extra day. – [III],
And 400 years = 20 extra days + 1 day
= 21 days = 3 weeks means 0
extra days. – [IV],
The above we will consider as century codes for our calculation.”
The students were listening attentively to Abhas sir’s explanations.
“Now coming to the months,
January, March, May, July, August, October and December have 31 days, which means (28+3) days = 4 weeks + 3 days, that is these months have 3 extra days.
Similarly, April, June, September and November have 2 extra days.
February has 0 extra days in an ordinary year and 1 extra day in a leap year.
Now, to make the calculation easier we will give codes to the months. Considering January as 0 and making cumulative additions, the codes will be obtained. For example, for May the code is Jan 3 + Feb 0 + Mar 3 + Apr 2 (extra days) = 8, which means, 1 week + 1 day. Therefore, the code for May is 1.
Similarly, the codes for the months are –
January – 0,
February – 3,
March – 3,
April – 6,
May – 1,
June – 4,
July – 6,
August – 2,
September – 5,
October – 0,
November – 3
December – 5
Finally, the weekday codes. Sunday-1, Monday-2, Tuesday-3, Wednesday-4, Thursday-5, Friday-6, and Saturday-0.” Abhas wrote everything on the blackboard with different colour chalks.
“Let’s take Prakriti’s birthday, 01 April 2004.
This is 2000 + 04 + April + 01
2000 is divisible by 400, therefore 0 extra days. In four years, there are three ordinary years and one leap year, therefore 3×1 + 1×2 = 5 extra days. The code for April is 06, and the date is 1.
Therefore 0+5+6+1= 12
Now when we divide 12 by 7, the remainder is 5 and the weekday code for 5 is Thursday, hence Prakriti was born on a Thursday.”
“Oh! This is not as complicated as I thought, just have to remember a few codes,” said Prakriti.
Prapti, the polymath of the class stood up and asked, “Sir, my father was born on 20 Aug 1973, it was a Monday. Here how would you calculate the century code and year code, because in Prakriti’s case it was 2004, the calculation was easier.”
“Good question, please sit down,” said Abhas. “We will write the date this way 1900+73+August+20. As I told you, every 400th year has 0 extra days, therefore 1900 = 1600 +300
= 4×400+300
= 0 extra days + 300; the century code for 300 is 1 – (a)
Next, in 73 years there are 55 ordinary years and 18 leap years, therefore we have [55×1 + 18×2] = {55+36] = 91 extra days. – (b)
The code for August is 02. – (c)
Therefore, the calculation for 20 Aug 1973 = 1+ 91+2+20=114.
114 divisible by 7 gives remainder 2, and the weekday code for 2 is MONDAY.”
“Sir, Netaji Subhash Chandra Bose was born on 23 January 1897, can you find the day?” asked sambit.
“Let’s calculate, Sambit, 23 January 1897
=1800 + 97 + January +23
= [1600 + 200] + [97 + 24] + 0 + 23
= [0+3] + [121] + 23 (Because 1600 has 0 extra days and century code for 200 is 3, that is 3 extra days and 97 when divided by 4 gives quotient 24.
= 147 and 147 when divided by 7 leaves remainder 0 and the weekday code for 0 is Saturday, therefore Netaji was born on a Saturday,” explained Abhas.
Elen stood up, he was perplexed and asked, “Sir, my mother was born on 20 January 1976 and she once said it was a Tuesday, but I am unable to get the answer, my procedure is correct…”
With a broad smile, Abhas replied, “I was just about to provide you all with an example that defied this rule we have been following so far and you gave it to me. While calculating for a leap year, if the date is in January or February then make sure to subtract 1 from the total. I leave you to think why we must subtract 1. Ponder over and let me know in the next class. Now coming to 20 January 1976.
= 1900 + 76 + January +20
= [400×4+300] + [76+19] + 0 + 20
= 1+ 95 + 20 (century code for 300 is 1 and 400 is 0 and code for January is 0)
= 116, as per the rule of subtracting 1, we have 116-1 = 115.
Dividing 115 by 7, we have the remainder 3.
And the weekday code for Tuesday is 3. Therefore, 20 January 1976 is Tuesday.”
Prakriti was ecstatic and replied, “Sir, I got how my sister’s birthday is Wednesday because 13 October 2010 = 0 + 12+ 0 +13 = 25, and the remainder is 4, and the code 4 stands for Wednesday.”
“Excellent, you have understood the trick,” said Abhas sir. “You know well when India became independent. Can you find the day? And remember not to forget the extra class in lieu of this period. There are many other calculations which can be made easier using this technique, will explain them to you some other time.”
As the bell rang and Abhas sir was about to leave, Sambit responded, “Excuse me, sir, 1947 August 15 was a Friday because the sum is 76 (1+58+2+15) and the remainder is 6 which stands for Friday.
Abhas showed a thumbs up to Sambit as he left the class.
The entire class was busy finding the day for the birth dates throughout their free periods. High-fives, fists punching the air, and a lot of positive gestures were conspicuous in their classroom.
The author is an enthusiastic educator of mathematics and writes on topics related to innovative and engaging educational methods. He is a CBSE resource person for teacher professional development programmes. He is known for his creative skills, story writing, dramatic and mimicry abilities, and contributions as a community worker. He can be reached at anilpatnaik8@gmail.com.