Brain Teasers
12 Days of Christmas
How many gifts, in total, did I receive during the Twelve Days of Christmas - according to the song?
Answer
364; for example, on the fifth day of Christmas, my true love gave to me: five gold rings + four calling birds + three French hens + two turtle doves + a partridge in a pear tree.Hide Answer Show Answer
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Comments
Does the pear tree count?
Depends how nice the women and men were to you doesn't it?... (not like that) I mean they could have been festive and brought presents themselves.
tree and the bird are the same... i think
Yeah, I think the partridge and the tree it was in are a package deal. It's fairly simple to calculate as 1 gift is given 12 times, 2 (turtle doves) are given eleven times, and so on up to 12 gifts are given once. thus you have (1*12)+(2*11)+(3*10). . .(10*3)+(11*2)+(12*1). So if you figure up to half way of this calculation (. . .+(6*7)), then double that total you get the answer.
so...wow..i see..interesting
so...that would be a tetrahedral number?
I recognized these as the tetrahedral numbers, but I didn't remember the formula, so I did it the same as Paul. The formula is:
f(n) = n(n+1)(n+2)/6
so
f(12) = 12(12+1)(12+2)/6
= 12*13*14/6
= 2*13*14 = 364
f(n) = n(n+1)(n+2)/6
so
f(12) = 12(12+1)(12+2)/6
= 12*13*14/6
= 2*13*14 = 364
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