Twelfth

Question
What was given on the fourth day of Christmas?
Answer:
Calling birds

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.