As is known, Beis Shammai lights eight lights on the first night of Chanukah, seven on the next, and so on decreasing by one each night.
But why? Once there was a follower of Beis Shammai who lit candles this way to mirror the bulls of Sukkos: 13 the first day and decreasing by one each day afterward.
Imagine, if you will, a 13-branched menorah (representing this connection) with 8 candles....
Significance of choosing 8 from 13
There are 1,287 different ways to pick 8 branches for lights out of 13.
1 + 2 + 8 + 7 = 18 (chai/life)
1,287 is also the gematria of the pasuk "hashem maon atah/gd you are a refuge". On Sukkos, we remember that gd is our true refuge by living in temporary shelters. On Chanukah, Beis Shammai acknowledges gd as our true refuge by diminishing light.
13 is the gematria of echad/one. When we take this oneness and divide it among 8 lights, we get 13/8 = 1.625. The distance between this and one-ness is 625 = 25^2. Chanukah occurs on the 25th of Kislev.
How to choose?
One minhag is to associate each of the 13 branches with one of the 13 attributes of mercy. Each Chanukah, Jews who follow this minhag select the attributes they most need in this time of winter darkness. Those branches are the branches that receive the candles.
But what is the sod?
13/8 is the time signature of "skimbleshanks the railway cat"





