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)?
13 years ago
13 years ago
the 14th day
11 months ago
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.