Answering Exams

What was given on the fourth day of Christmas?

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.

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