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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?

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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. ;)

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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

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