## Monday, 1 January 2018

### One the first day of Christmas my true love gave to me...

Yes, Christmas maybe over, but the puzzles still remain! During our Christmas episode Thomas provided the following puzzle.

In the song "12 days of Christmas" how many presents do you get over all?

Note the lyrics are given below, but the main idea is that you are adding up consecutive triangular numbers. Namely, on the first day you get 1 present. On the second day you get 3 = 2+1 more presents, making 4 overall. On the third day you get 6 = 3 + 2 + 1 more presents, meaning 10 overall. Thus, in total, how many presents do you get?

You can find the answer during Maths At: Christmas

We also gave you a bonus question that built on this ideas.

In the song "12 days of Christmas" how many legs are there in total?

As we discussed in the podcast there are many possible solutions to this question based on different assumptions. Do the milk maids have stools? Has a swan lost a leg and swimming in a circle?

Many possibilities! We will reveal our solution next time.

For those who want a consistent set of lyrics we used the following list:

First day:
A Partridge in a Pear Tree

Second day:
2 Turtle Doves
and a Partridge in a Pear Tree

Third day:
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Fourth day:
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Fifth day:
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Sixth day:
6 Geese a Laying
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Seventh day:
7 Swans a Swimming
6 Geese a Laying
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Eighth day:
8 Maids a Milking
7 Swans a Swimming
6 Geese a Laying
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Ninth day:
8 Maids a Milking
7 Swans a Swimming
6 Geese a Laying
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Tenth day:
10 Lords a Leaping
8 Maids a Milking
7 Swans a Swimming
6 Geese a Laying
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Eleventh day:
11 Pipers Piping
10 Lords a Leaping
8 Maids a Milking
7 Swans a Swimming
6 Geese a Laying
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree

Twelfth day:
12 Drummers Drumming
11 Pipers Piping
10 Lords a Leaping
8 Maids a Milking
7 Swans a Swimming
6 Geese a Laying
5 Golden Rings
4 Calling Birds
3 French Hens
2 Turtle Doves
and a Partridge in a Pear Tree