# Twelve Days of Christmas

Pro Problems > Math > Statisics and Probabilities > Counting Principles## Twelve Days of Christmas

We all know the song "The Twelve Days of Christmas," and how the gift giving works:

Day One: 1 partridge in a pear tree

Day Two: 2 turtle doves *and *1 partridge in a pear tree

Day Three: 3 calling birds, 2 turtle doves, and 1 partridge in a pear tree

Thus, after three days, the singer has 1 + 3 + 6 = 10 gifts. [Note that some people interpret the song as 1 gift the first day, 2 the second day, three the third day, etc., but that is not what the song *says*, so we will go with the literal interpretation of the song!]

After Mrs. Claus heard the elves singing this song one Christmas, she decided that the next year she would take this song to the extreme, and extend it to 20 days of Christmas, giving gifts (in the same pattern as the song) for 20 days.

Santa Claus caught wind of what she was doing and, since he is considered to be the epitome of the spirit of giving at Christmas time, decided he couldn't be out-given, and did the 25 days of Christmas instead.

By how many gifts did Santa "outgive" Mrs. Claus?

## Solution

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[No calculators, please]