The 12 Days of Christmas is all very well as a song, but why is the narrator so coy about what happened on the 13th day of Christmas? Or, indeed, the days after that? Assuming that the first Christmas was on Christ’s birth (on December 25, 1 AD, obviously), there are a maximum of 734,742 days of Christmas to fill. This may be tricky, but not impossible.
On the 734,742nd day of Christmas, my true love gave to me…
734,742 grains of sand
734,741 bits of lint
A la-a-arge bag of rice…
The main issue is that the true love presumably has to keep giving the gifts he has given on previous days. By the end of the 12 days he has given 12 drummers drumming, 22 pipers piping, 30 lords a-leaping, 36 ladies dancing, 40 maids a-milking, 42 swans a-swimming, 42 geese a-laying, 40 gold rings, 36 calling birds, 30 French hens, 22 turtle doves and 12 partridges in 12 pear trees.
If the gift giving carried on long term, which gift would be the limiting factor? Geese do not lay all year round, but usually they only lay in spring anyway, so the true love must already have found a way to overcome that. Without doing calculations for how many hens there are in France, I think it is reasonable to say that the lords are the problem. There are only 798 in Britain at the moment, so excluding foreign lords and people with the surname Lord, you would run out on day 88.