How many candles in total are lit on the Menorah for the eight days of Hanukkah?
If you answered 44, you are correct, but how long did it take you to arrive at that number? If it was more than 30 seconds, then you probably added up all the numbers from one to eight, and then added eight shamas candles (the candle from the upper or lower branch that is used to light the other eight candles). If you were faster than that, you probably knew how to use Gauss’ formula.
Carl Friedrich Gauss (1777-1855) is recognised as one of the greatest mathematicians of all time, having made significant contributions to almost every area of mathematics, as well as physics, astronomy and statistics. And like many well known mathematicians, Gauss displayed striking mathematical prowess from a young age, with many stories illustrating how clever was.
One such tale – and a favourite among math teachers! – suggests Gauss' teacher asked his class to add together all the numbers from 1 to 100, assuming that this would occupy them a while. He was shocked when young Gauss, after a few seconds thought, wrote down the correct answer 5050. The teacher couldn't understand how his pupil had calculated the sum so quickly in his head, but eight year old Gauss declared the problem was actually quite simple.
He had added the numbers in pairs - the first and the last, the second and the second to last and so on, observing that 1+100=101, 2+99=101, 3+98=101. The total would therefore be 50 lots of 101, which is 5050.
Gauss's method forms a general formula for the sum of the first n integers, namely that 1+2+3+…+n = 0.5n x (n+1)
Using this formula, we can quickly calculate the total number of candles lit on Hanukkah. One candle is lit on day one, two on day two... continuing until day eight. Using Gauss’s formula, 8/2 x (8+1)=36. Plus eight shamas candles gives 44.
Have fun showing off your new holiday-themed mathematical skills and Happy Hanukkah!