12 Days Of Christmas Puzzle - Solution

The Puzzle:

According to the traditional song, on the first day of Christmas (25th December), my true love sent to me:

• A partridge in a pear tree

On the second day of Christmas (26th December), my true love sent to me THREE presents:

• Two turtle doves
• A partridge in a pear tree

On the third day of Christmas (27th December and so on) my true love sent to me SIX presents:

• Three French hens
• Two turtle doves
• A partridge in a pear tree

This carries on until the the twelfth day of Christmas, when my true love sends me:

• Twelve drummers drumming
• Eleven pipers piping
• Ten lords a-leaping
• Eight maids a-milking
• Seven swans a-swimming
• Six geese a-laying
• Five gold rings
• Four calling birds
• Three French hens
• Two turtle doves
• A partridge in a pear tree

After the twelve days of Christmas are over, how many presents has my true love sent me altogether?

Our Solution:

Day by Day:
1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 presents

Which is really interesting when you think there are 365 days in a typical year!

A kind reader, Martin J. Fowler, found this interesting symmetry in the total number of each present:

12 Partridges (12 days x 1)
22 Turtle Doves (11 days x 2)
30 French Hens (10 days x 3)
36 Calling Birds (9 days x 4)
40 Gold Rings (8 days x 5)
42 Geese Laying (7 days x 6)
42 Swans swimming (6 days x 7)
40 Maids a Milking (5 days x 8)
36 Ladies dancing (4 days x 9)
30 Lords a Leaping (3 days x 10)
22 Pipers Piping (2 days x 11)
12 Drummers drumming (1 day x 12)

Puzzle Author: Stephen Froggatt

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