Fun And Puzzles


1. 12 Days Of Christmas 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 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 A partridge in a pear tree
After the twelve days of Christmas are over, how many presents has my true love sent me altogether?

Show Answer
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)

2. Mirror, Mirror Puzzle

If you continue shading the squares so that the two dotted lines become lines of symmetry (mirror lines) of the completed diagram, how many squares will be left unshaded?


Show Answer
If you continue shading the squares so that the two lines become mirror lines, we get this:
(Note: I have shaded the new squares differently just so that you can see where they go.) The number of squares left is then 9.
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