Holiday challenge!

Ask the Community
#1

Our team participated in a remote trivia event this week, of course using Coda docs to collaborate on answers. :grinning_face_with_smiling_eyes:

One of the questions referred to the song “The Twelve Days of Christmas”. If you haven’t heard it, the lyrics run through a list of gifts each day. (Full lyrics here.) The question asked: How many gifts were given in this song?

The general idea is that on the first day, you receive 1 gift of x. On the second day, you receive 2 gifts of y and 1 gift of x. On the third, you receive 3 gifts of z, 2 gifts of y, and 1 gift of x.

1
1 + 2
1 + 2 + 3
1 + 2 + 3 + 4
…
Until the final day: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Our team came up with some fun formulas to get to the answer, so I thought it would be a fun challenge to pose here. Let us know what you come up!

6 Likes
#2

Sequence(1,12).FormulaMap(Sequence(1,CurrentValue).Sum()).Sum()

2 Likes
#4

Hint: Gauss figured this out in elementary school (sort of)
Other hint: It’s also related to the number of edges in a fully connected graph
Edit: I was wrong. It’s the triangular numbers, not the number of edges in a fully connected graph

3 Likes
#5

Did I get it right?
Another way:

There are 12 * 1, 11 * 2, 10 * 3…
Σ(1,12)[13-n]*n
Sequence(1,12).FormulaMap((13-CurrentValue)*CurrentValue).Sum()

3 Likes
#6

As Paul said before deleting their post (not sure why?), there is also a way to do it without FormulaMap

Also, @Breno_Nunes, it might be nice to blur your answers to save people from the spoilers in case they want to take a shot. You can do that like this:
image

3 Likes
#7

I didn’t even know it was possible. Thank you.

1 Like
#8

I got confused at first. To simply calculate the sum of 1 + 2 + … + N, there’s an arithmetic progression sum formula (1 + N) * (N / 2) (because 1+13 + 2+11 + 3+10… i.e. 13 x half the numbers.

But then I saw that I had to sum the progressions themselves as well. So this formula isn’t really relevant here.

I still have a feeling that it can be simplified to a polynomial that doesn’t have to use loops

#9

There is indeed a polynomial expansion: see link.

But the loops method is fun. Anyone use WithName() to do it?

3 Likes
#10

Ha cool, knew it! The tetrahedra explanation is awesome.

Loops is fun, but a simple polynomial is efficient :wink: and I favor efficient.

2 Likes
#11

One way to do it using WithName:

WithName(Sequence(1,12), Twelve, 
  Twelve.FormulaMap(
    WithName(CurrentValue, CurrentDay, 
      Twelve.Slice(1, CurrentDay).Sum()
    )
  )
).Sum()

I guess this is similar to @Breno_Nunes’ first solution, except WithName allows us to reuse the initial array and take slices of it, instead of making a new one.

One of the nice things about WithName is it helps to make formulas a bit more self-documenting

1 Like