How Many Gifts Do I Get Over the Twelve Days of Christmas?
'The Twelve Days of Christmas' is perhaps one of the most famous and most often sung Christmas carols of all.
It tells the tale of a person receiving gifts from their true love on each of the 12 days following Christmas. They start off on the first day with just one gift—a partridge in a pear tree. On day two, as well as the partridge, they receive two turtle doves. On day three, they also get three French hens on top of the presents already mentioned.
This continues until day 12 when we finish with the following verse:
On the twelfth day of Christmas
My true love sent to me
Twelve drummers drumming
Eleven pipers piping
Ten lords a-leaping
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five gold rings
Four calling birds
Three French hens
Two turtle doves
and a partridge in a pear tree.
So, just how many gifts are in the 12 days of Christmas? It sounds like quite a bit. Let's find out the exact number.
It tells the tale of a person receiving gifts from their true love on each of the 12 days following Christmas. They start off on the first day with just one gift—a partridge in a pear tree. On day two, as well as the partridge, they receive two turtle doves. On day three, they also get three French hens on top of the presents already mentioned.
This continues until day 12 when we finish with the following verse:
On the twelfth day of Christmas
My true love sent to me
Twelve drummers drumming
Eleven pipers piping
Ten lords a-leaping
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five gold rings
Four calling birds
Three French hens
Two turtle doves
and a partridge in a pear tree.
So, just how many gifts are in the 12 days of Christmas? It sounds like quite a bit. Let's find out the exact number.
Xavier Romero-Frias
https://commons.wikimedia.org/wiki/File:XRF_12days.jpg
How Many Gifts Would I Receive Each Day?
One way to tackle the question of how many gifts you are receiving is to look at how many gifts are being received each day.
On day one, this is simple: just the one gift.
On day two, we get 1 + 2 = 3 gifts.
On day three, we get an additional three gifts on top of day two's three. We receive 3 + 3 = 6 gifts.
On day four, we add four to the previous day's total, getting 6 + 4 = 10.
This continues all the way to 12. For each day, we add that day's number to the tally from the previous day, giving us the totals in the table below.
On day one, this is simple: just the one gift.
On day two, we get 1 + 2 = 3 gifts.
On day three, we get an additional three gifts on top of day two's three. We receive 3 + 3 = 6 gifts.
On day four, we add four to the previous day's total, getting 6 + 4 = 10.
This continues all the way to 12. For each day, we add that day's number to the tally from the previous day, giving us the totals in the table below.
Day Number |
Total Number of Gifts Received on This Day |
1 |
1 |
2 |
3 |
3 |
6 |
4 |
10 |
5 |
15 |
6 |
21 |
7 |
28 |
8 |
36 |
9 |
45 |
10 |
55 |
11 |
66 |
12 |
78 |
The Total Number of Gifts Received
By adding up each of the numbers in the 'Total number of gifts received' column, we find we receive a whopping 364 presents in total. That's only one short of a gift a day for an entire year.
The Mathematics Behind the Totals
The number of gifts given each day follows an interesting mathematical pattern. Let's take a closer look.
Day 1 - 1
Day 2 - 1 + 2 = 3
Day 3 - 1 + 2 + 3 = 6
Day 4 - 1 + 2 + 3 + 4 = 10 and so on.
This sequence, 1, 3, 6, 10, 15, 21, … , where the amount being added increases by one each time, is known as the triangular numbers, so called because we can create triangles by having 1 dot in the top row, 2 dots in the second row and so on as in the image below.
Day 1 - 1
Day 2 - 1 + 2 = 3
Day 3 - 1 + 2 + 3 = 6
Day 4 - 1 + 2 + 3 + 4 = 10 and so on.
This sequence, 1, 3, 6, 10, 15, 21, … , where the amount being added increases by one each time, is known as the triangular numbers, so called because we can create triangles by having 1 dot in the top row, 2 dots in the second row and so on as in the image below.
Melchoir - Wikimedia Commons
Tetrahedral Numbers and the Twelve Days of Christmas
We get another interesting sequence of numbers if we keep a running total of all of the gifts received up to and including each day. Take a look at the table below. In this table, as well as the number of gifts received each day, I have also put a running total in the right-hand column by adding together all of the numbers up to and including that day.
Day Number |
Total Number of Gifts Received on This Day |
Total Number of Gifts Received By This Day |
1 |
1 |
1 |
2 |
3 |
4 |
3 |
6 |
10 |
4 |
10 |
20 |
5 |
15 |
35 |
6 |
21 |
56 |
7 |
28 |
84 |
8 |
36 |
120 |
9 |
45 |
165 |
10 |
55 |
220 |
11 |
66 |
286 |
12 |
78 |
364 |
The numbers appearing in the right-hand column form a sequence known as the tetrahedral numbers. Just like the triangular numbers are so called as they form triangles, the tetrahedral numbers are how many spheres (balls) are needed to make a tetrahedron (otherwise known as a triangular-based pyramid).
What About the Total Number of Each Gift?
We have seen so far that, at the end of the 12 days, we have a grand total of 364 gifts. We have also seen how many gifts we receive each day and how many gifts we will have received in total up to each day. But what about how many of each type of gift?
The partridge in the pear tree is easy. We get one of these on each of the twelve days; hence, we end up with 1 × 12 = 12 partridges in pear trees.
We receive two turtle doves on each day apart from the first day, making 11 days, and so receive 2 × 11 = 22 turtle doves.
We receive three French hens on each day apart from the first two days, making 10 days and so receive 3 × 10 = 30 hens.
This continues following the same pattern; as the day number increases by one, the number of times it is gifted decreases by one. Mathematically, this can be represented as so:
For a gift that is first received on the nth day:
Total number = n × (13 − n)
Using this formula, the total number of each gift has been calculated in the table below. You can see that the numbers form a pleasingly symmetrical pattern.
The partridge in the pear tree is easy. We get one of these on each of the twelve days; hence, we end up with 1 × 12 = 12 partridges in pear trees.
We receive two turtle doves on each day apart from the first day, making 11 days, and so receive 2 × 11 = 22 turtle doves.
We receive three French hens on each day apart from the first two days, making 10 days and so receive 3 × 10 = 30 hens.
This continues following the same pattern; as the day number increases by one, the number of times it is gifted decreases by one. Mathematically, this can be represented as so:
For a gift that is first received on the nth day:
Total number = n × (13 − n)
Using this formula, the total number of each gift has been calculated in the table below. You can see that the numbers form a pleasingly symmetrical pattern.
The Totals of Each Type of Gift
Gift |
Calculation |
Total Number Received |
Partridges in pear tress |
1 × 12 |
12 |
Turtle doves |
2 × 11 |
22 |
French hens |
3 × 10 |
30 |
Calling birds |
4 × 9 |
36 |
Gold rings |
5 × 8 |
40 |
Geese a-laying |
6 × 7 |
42 |
Swans a-swimming |
7 × 6 |
42 |
Maids a-milking |
8 × 5 |
40 |
Ladies dancing |
9 × 4 |
36 |
Lords a-leaping |
10 × 3 |
30 |
Pipers piping |
11 × 2 |
22 |
Drummers drumming |
12 × 1 |
12 |
364 Gifts in 12 Days!
So there we have it. Over the 12 days of Christmas, your true love has given you a total of 364 gifts which includes a incredible 42 geese and, stranger still, 30 leaping lords!
What do you think? Add your comments below.
What do you think? Add your comments below.