Counting all the Chanukah Candles in 5783/2022: Another Calendrics Blog Post

Yom sheni, 18 Kislev, 5783.

David Orenstein, Emeritus, Danforth CTI,
Toronto, Ontario, Canada
BSHM Education Committee Member
david.orenstein@alumni.utoronto.ca

Next Monday will be Yom sheni, 25 Kislev, 5783, and we’ll already be celebrating Chanukah. The second lighting will be that evening, while the first would have been at the previous sunset, the first of eight nights of Chanukah for 5783. And we’ll continue until the spectacular last lighting at the sunset that begins Yom sheni, 2 Tevet, 5783.

Celebration will include the lighting of the candles on the Menorah, the candelabra with places for up to eight candles, plus the Shamash, the candle which is responsible for lighting the candles that celebrate the Miracle of Chanukah.

This last lighting will also be on the evening of Sunday, December 25, 2022; Christmas Day in the Gregorian Calendar.

So, how many candles do you have to light to complete the celebration of the Chanukah miracle each year at this time? 

In fact, when I was teaching, I’d regularly included this as a bonus question on tests and quizzes in Chanukah season.

You can approach this question in several ways.

1) Brute force:
Number of Chanukah candles for all eight nights
= 1st Night+ 2nd Night+ 3rd Night+ 4th Night
 + 5th Night+ 6th Night + 7th Night+ 8th Night
= (1+1) + (1+2) + (1+3) + (1+4) 
+ (1+5) + (1+6) + (1+7) + (1+8)
= 2 + 3 +4 + 5 + 6 + 7 + 8 + 9
= (2 + 3) + (4 + 5) + (6 + 7) + (8 + 9) 
= (5 + 9) + (13 + 17) 
= 14 + 30 
= 44.

2) Separating the Shamashes from the Others:

Number of Shamashes for Eight Nights + Sum of First Eight Natural Numbers
= (1 +1 +1 + 1 + 1 + 1 +1 +1) + Sum of i where i runs from 1 to 8
= 8 + (n+1)n/2 [where n = 8]
= 8 + (8+1)8/2
= 8 + (9)4
= 8 + 36
= 44

3) Spotting a Pattern and Grouping:

As in Method 1) Starting from 3rd Equals Sign
= 2 + 3 +4 + 5 + 6 + 7 + 8 + 9
= (2 + 9) + (3 + 8) + (4 + 7) + (5 + 6)
= 11 + 11 + 11 + 11
= 4(11)
= 44

4) Advanced Formula:

Sum of First Nine Natural Numbers – The Shamash that’s Not Lit Before the First Night
= Sum of i where i runs from 1 to 9 – 1
= (n+1)n/2 [where n = 9] – 1
= (9 + 1)9/2
= (10)4.5
= 45 – 1
= 44

5) Experiential:

Go Buy a Box of Chanukah Candles to Light your Menorah
= Read the Box
= “44 Candles”

That gives you 44 as the total number of candles for an eight-day Festival of Lights, but in what order do you light them? 

But that’s another story!

Happy Chanukah!

Links

Previous BSHM Calendrics Posts:
Re-reading Torah and Mathematics Texts for 5783 / 2022 (and 2023), November 28, 2022.
https://www.bshm.ac.uk/re-reading-torah-re-reading-science-texts-57832022-2023-another-calendrics-blog-post

Re-reading the Torah in 5783 post, November 21, 2022.
https://www.bshm.ac.uk/re-reading-torah-5783-another-calendrics-blog-post

Rosh Ha-Shonah 5783 post, September 6, 2022.
https://www.bshm.ac.uk/my-many-new-years-another-calendrics-blog-post

Passover/Easter post, April 15, 2022.
https://www.bshm.ac.uk/happy-easter-happy-passover

Previous CSTHA Calendrics Blog Posts:
Re-reading Torah and Canadian Science Texts for 5783 / 2022 (and 2023), November 25, 2022.
https://cstha-ahstc.ca/2022/11/25/75314/

Simchat Torah 5783 post, October 26, 2022.
https://cstha-ahstc.ca/2022/10/26/its-simchat-torah-5783-another-calendrics-blog-post/

Putting “Calendrics” in CSTHA “Search” function.
https://cstha-ahstc.ca/?s=Calendrics

Bibliography

Albert Pietersma and Benjamin G. Wright (eds.) (2007), A New English Translation of the Septuagint, Oxford University Press, New York. xx + 1027 pp., incl four Books of Maccabees:

George T. Zerros, “1 Makkabees”, p. 478-502.
Joachim Schafer, “2 Makkabees”, p. 503-520.
Cameron Bord-Taylor, “3 Makkabees”, p. 521-529.
Stephen Westerholm, “4 Makkabees”, p. 530-541

Irving Greenberg (1988) “Assimilation, Acculturation, and Jewish Survival: Hanukkah”. p. 258-282, in The Jewish Way.

-(1988) The Jewish Way, Summit Books, London. 463 pp., incl. 13 pp. annotated biblio., 7 pp. Glossary of Names, 15 pp. index.