If you get all of the presents in the song “The Twelve Days of Christmas,” how many presents do you get?
364 (because of the AND)
Here’s the formula: ((1 x 12)+ (2 x 11)+(3 x 10)+(4 x 9)+(5 x 8)+(6 x 7)) x 2
You get the partridge all twelve days, the two turtle doves for eleven, the three French hens for ten days, etc. After the six geese a-laying, which you get for seven days, you get seven swans a-swimming for six days, eight maids a-milking for five days, etc. so you can stop the sequence at the halfway point and multiply by two.
This is all well and good unless you assume that the implied AND is a carryover from the previous day. Then you only get (1 + 2 + 3 + 4 + 5 + 6 +7 + 8 + 9 + 10 +11 + 12) or 78, which is (6 X 13) because of there are six pairs that equal 13 (1+12), (2+11), etc.
Which number you choose depends on how you interpret the song. Is “On the twelfth day of Christmas, my true love gave to me…12 Drummers Drumming, 11 Pipers Piping, 10 Lords-a-Leaping, 9 Ladies Dancing, 8 Maids-a-Milking, 7 Swans-a-Swimming, 6 Geese-a-Laying, 5 Golden Rings, 4 Colly Birds, 3 French Hens, 2 Turtle Doves, and a Partridge in a Pear Tree” interpreted with as a noun phrase with the commas representing ANDs.
Or is the lyric understood as an elliptical coordination, shorthand for “On the twelfth day of Christmas, my true love gave to me…12 Drummers Drumming, [and on the eleventh days of Christmas, my true love gave to me] 11 Pipers Piping, [and on the tenth day of Christmas, my true love gave to me] 10 Lords-a-Leaping, [and on the ninth day of Christmas, my true love gave to me] 9 Ladies Dancing, …, etc.”
The arithmetic depends on the grammar. As it usually does.