364
it goes like this
1st day = 1
2nd day = 3
3rd day = 6
4th day = 10
5th day = 15
6th day = 21
7th day = 28
8th day = 36
9th day = 45
10th day = 55
11th day = 66
12th day = 78
You'd be correct, except for one thing: you didn't take into account that on each of the 12 days, you would receive one partridge AND one pear tree, thus making it necessary to add the 12 additional pear trees for a total of 376 gifts. On the other hand, if your true love gave you only ONE pear tree and simply added birds to it each day, you would get 365 gifts, or one gift for every day of the year. Romantic, huh?
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