# Formula for 12 days of Christmas?

If you were to substitute exercises for gifts in the song 12 days of christmas. And then perform them for every mention in the verse. For example..

• on the 12th day 12 pushups=12
• on the 11th day 11 situps=22
• on the 10th day 10 jumping jacks=30

Is there a formula to express this?

-
add comment

## 1 Answer

I'm not sure what you mean. Are you asking about something like $(13-n)\cdot n$?

To derive this, see that $n$-th verse is repeated $(13-n)$ times, so if you do the exercise associated to $n$-th verse $n$ times each time it is repeated, you do it $(13-n)\cdot n$ times in total.

Doing these exercises in the pacing the song is usually sung in would be quite the superhuman feat though... ;)

Anyway, changing the words doesn't really change the calculation. The only thing that changes is whether you do 30 jumping jacks or get 30 lords a leaping. ;)

-
As a child it drove me crazy that people sang the things you got on the various days in different orders depending on who you asked. –  user29743 Dec 23 '12 at 17:40
add comment