Main Page
(x, why?)
by Chris Burke
Mr. Burke's Math logo

952: Pascals Triangle
Comic
Click Me
for a random comic
Mr. Michael Keegan, Math Teacher

The 14C3 gifts of Christmas?

This occurred to me a while ago, but after Christmas, and I decided that it couldn't wait until December. (And I'd likely forget about it.)

While coming up with mathematical formulas and computer code for calculating this number, I overlooked a a very reliable reference tool: Pascal's Triangle.

It has more uses than simply expanding polynomials because of its many properties.

Some of these properties are as follows:

  • The "zeroth" element of each row is the number 1.
  • The first element of each row is the number of the row (keeping in mind that the top row is Row 0).
  • The second element of each row is are the consecutive triangle numbers, the sum of the consecutive numbers before it.
  • Which makes the third element of each row the sum of the consecutive triangle numbers.
  • And, finally, the position of each element in Pascal's Triangle corresponds to the number of Combinations designated by the notation nCr where n is the row and r is the element of that row.

    What this means is that for any given day in that song (The Twelve Days of Christmas):

  • nC1 refers to the day we're up to. On Day 7, 7C1 is 7.
  • n+1C2 refers to the total number of gifts given on the nth day. On Day 7, 8C2 is 28.
  • n+2C3 refers to the total number of gifts given altogether up to the nth day. On Day 7, 9C3 is 84.

    Applying this to the 12th day of the song:

  • 12C1 is 12.
  • 13C2 is 78.
  • 14C3 is 364.

    And I could've been finished a whole lot sooner. But I wouldn't have gotten a recursive comic out of that.

    One last thing: Did you ever try to make a poster of Pascal's Triangle? Have your students tried to do it for a math fair? The numbers start to get really big in the middle, really fast. (That's a post for another day.) But that's also why the poster in this comic is so large! Otherwise, it wouldn't be readable (and I had to modify the "364" so you could find it easily!).


  • Please visit my blog: http://mrburkemath.blogspot.com.
    (You can also go there to leave comments!)
    First comic Previous comic Next comic Latest comic
    Click Me
    for a random comic
    Kitt Ten. A walking, talking numeral
    The Webcomic List

    DEC Jan 2015 FEB
    28 29 30 31 1 2 3
    4 5 6 7 8 9 10
    11 12 13 14 15 16 17
    18 19 20 21 22 23 24
    25 26 27 28 29 30 31
    1 2 3 4 5 6 7





    (x, why?) is hosted on ComicGenesis, a free webhosting and site automation service for webcomics.
    (x, why?)