Zeller’s Congruence – A handy tool for travellers / randonneurs

Well, this may be arguable.

How much of it is useful really depends on how you take it.

However, I believe its worth learning it than depending on gadgets that brood over battery and network. Often travelling, we remember the dates, but tend to forget the days of the week, ie Sunday or Monday or hence on..

Lately, I came across Zeller’s congruence. The algorithm amazed me. Its quick, simple and fun-to-do (especially if you have a thingy for numbers :p)

Zeller’s congruence algorithm is all about finding which day of the week is for a given day of a month.

Like for instance, say today is 27th of July, 2015

And I want to find which day of week is it. So here is how –

Step 1: take last two digits (unit place and ten’s place) of the year. The year is 2015 so its 15

Step 2: Divide the year by four. If its divisible, then the year is a leap year. If so, follow step 3 or else skip it.

Step 3: If the year is leap year (in case of 2015, its not) then add one from the last two digits.

Step 4: Continued from step two, Dividing by 4, 15 / 4 = 3.75 (leave the decimal part) = 3 (a non-zero number and hence we won’t subtract one as per step 3)

Step 5: Add the remainder (here in our case, 3) to the last digits of year = 15 + 3 = 18

Step 6: Now add the day of the year to it. Ie., 18 + 27 = 45

Step 7: Add the number corresponding to month of the year from below table (now this my dear all, you have to memorize!)

Months Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec
Number 6 2 2 5 0 3 5 1 4 6 2 4

Tip: remember it like a credit card number 6225 0351 4624

So, in our case its July, so we will add 5 to our total. Ie., 45 + 5 = 50

Step 8: Keep subtracting seven from the total until you arrive at a remainder, which is between 1 to 7.

Ie., 50 – 7 -7 -7 -7 -7 -7 -7 = 1

The remainder answers the day of the week. One corresponds to Monday, two Tuesday and so on..

The remainder we got after subtracting sevens is 1, which corresponds to Monday!

And it is indeed Monday today 😀

Thank you for your time!

Keep riding:)

Ps: I learned about this from here do refer this if you fail to understand me (which is most likely :p)


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The original purpose of this blog was promoting city cycling and popularizing urban green belt corridors, which it did for it's first one and a half year, since the year of it's launch - 2014. Now-a-days, that is, since the last two years, I haven't been city commuting on my bike, thanks to my city earning the world's most air polluted region title. And thanks to the redesigning of City roads, those are forked under construction since last six months, loosing a green cover of a whooping 9,100+ trees and the rising construction dust hazards. And lastly thanks to El nino of 2015 and El nina of 2016. I don't know if I have missed any other reason. The theme of the blog, hence, changed, into a bit of my own ramblings covering topics, such as - my travel blogging, Social issues in India, Climate change & biodiversity conservation.

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