Math 300

Groupwork

The 12 Days of Christmas

Dr. Wilson

 

In the Christmas song, "The 12 Days of Christmas", how many total gifts does her true love give to her? The gifts are:

  1. A partridge in a pear tree,
  2. Two turtle doves,
  3. Three french hens,
  4. Four calling birds,
  5. Five gold rings,
  6. Six geese a-laying
  7. Seven swans a-swimming,
  8. Eight maids a-milking,
  9. Nine ladies dancing,
  10. Ten lords a-leaping,
  11. Eleven pipers piping,
  12. Twelve drummers drumming.

We could count the number of gifts she gets on each day.

On the first day she gets 1 gift

On the second day she gets 1 + 2 = 3gifts.

On the third day she gets 1 + 2 + 3 = 6 gifts.

On the fourth day she gets 1 + 2 + 3+ 4 = 10 gifts.

On the fifth day she gets 1 + 2 + 3+ 4 + 5 = 15 gifts.

On the sixth day she gets 1 + 2 + 3+ 4 + 5 + 6 = 21 gifts.

On the seventh day she gets 1 + 2 + 3+ 4 + 5 + 6 + 7 = 28 gifts.

On the eighth day she gets 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 = 36 gifts.

On the ninth day she gets 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 + 9 = 45 gifts.

On the tenth day she gets 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 gifts.

On the eleventh day she gets 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66 gifts.

On the twelfth day she gets 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11+ 12 = 78 gifts.

We add 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 gifts.

We are adding the triangular numbers. The triangular numbers can be found in Pascal's triangle, so we can use Pascal's triangle.