...*

Slow mealtime conversations can often lead to very random discussions. Known fact.

And it was hardly surprising when one such event somehow ended up concerning Christmas songs/carols. Specifically, the '12 days' one.

It was wondered whether the recipient in the song would end up getting the gift of each day on every successive day, ie, would you get one partridge on all 12 days, two turtle doves on 11 days, and so on. The wording of the song obviously implies so.

Assuming the above, it was then wondered how many total items of each gift would be received. Quick calculations revealed the following numbers
12 partridges in a pear tree,
22 turtle doves,
30 French hens,
36 calling (colly) birds,
40 gold rings,
42 geese a-laying...
and it was then realised that the numbers follow the exact reverse pattern from day 7 onwards.

This, if plotted using number of gifts on the y-axis and days on the x-axis, reveals to be a plateau-shaped graph (a double-point peak graph).

It was then conjectured as to whether there was a universal equation for calculating the total number of items for each individual gift. After several minutes of paper-napkin-scribbling, such an equation was indeed discovered. Which is -

N = d x ((12-d)+1)
where, d = number of the day the gift is received on**

Said equation applies even if there were more than 12 days (simply replace the '12' with the number of days of choice). Although, the above graph only works for even-numbered day-sets. For odd numbers, it will be a single-point peak graph.


....so now you know. Isn't your life wonderfully enriched? Aren't you just jumping around and going "Yes! Yes! It all makes sense now"? Do you not see the light now? Good, good. That is how it should be. Gifts are very welcome. Do make them expensive ones.


* There's a lovely title there, something to do with food and maths, but does it reveal itself? Like heck it does.
** Keep in mind that the number of the day on which the gift is received, is the same as the multiples by which the gift is given, ie, five rings given each day from the fifth day onwards.