Every year on the first day of Christmas my true love gives me one gift, a partridge in a pear tree. On the second day of Christmas my true love gives me a total of three gifts, two turtle doves and a partridge in a pear tree. This will go on until the twelfth day of Christmas when my true love gives me a total of 78 gifts given: 12 lords a-leaping, 11 ladies dancing, 10 pipers piping, 9 drummers drumming, 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. Today I’m at home “alone” with the gifts from my true love. Assuming each person, and each bird, has two legs what day of Christmas is it if there are now 200 legs in my home (not including mine)?

the eight day

the 14th day

To determine the day of Christmas based on the number of legs in your home, we can start by adding up the number of legs contributed by each gift on each day.

On the first day, the partridge in a pear tree has 2 legs.

On the second day, the two turtle doves contribute 4 legs, and the partridge adds another 2 legs, bringing the total to 6 legs.

Following this pattern, you can calculate the total number of legs for each subsequent day:

Third day: 6 legs + 6 legs + 2 legs = 14 legs

Fourth day: 14 legs + 8 legs + 2 legs = 24 legs

Fifth day: 24 legs + 10 legs + 2 legs = 36 legs

Sixth day: 36 legs + 8 legs + 2 legs = 46 legs

Seventh day: 46 legs + 14 legs + 2 legs = 62 legs

Eighth day: 62 legs + 8 legs + 2 legs = 72 legs

Ninth day: 72 legs + 18 legs + 2 legs = 92 legs

Tenth day: 92 legs + 20 legs + 2 legs = 114 legs

Eleventh day: 114 legs + 22 legs + 2 legs = 138 legs

Twelfth day: 138 legs + 24 legs + 2 legs = 164 legs

Now, we need to figure out which day of Christmas it is when there are 200 legs in your home. We can do this by comparing the total number of legs on each day with 200.

The day of Christmas when there are less than 200 legs is the 12th day, as it has a total of 164 legs. The next day, the 13th day, would exceed 200 legs.

Therefore, if there are now 200 legs in your home (not including yours), it means it is the 12th day of Christmas.