Aeolienne
Well-Known Member
I didn't win a prize for this, but I managed to answer a question in our office do's Christmas quiz which no-one else got right:
What is the total number of presents received from "my true love" over the Twelve Days of Christmas?
What is the total number of presents received from "my true love" over the Twelve Days of Christmas?
364.
If you listen to the words, the true love (or ex by now!) sends the recipient a new installment of presents each day plus a repetition of all the previous gifts. So the overall sum equals
1x12 + 2x11 + 3x10 + 4x9 + 5x8 + 6x7 +
7x6 + 8x5 + 9x4 + 10x3 + 11x2 + 12x1 = 364.
You can speed this up if you notice the symmetry in the above pattern; you need only calculate the addition sum up to the sixth day (182) and then double this interim result to get 364.
You could probably speed up the calculation even more by using a formula for triangle numbers, but I couldn't find one on Wolfram Mathworld when I last looked.
If you listen to the words, the true love (or ex by now!) sends the recipient a new installment of presents each day plus a repetition of all the previous gifts. So the overall sum equals
1x12 + 2x11 + 3x10 + 4x9 + 5x8 + 6x7 +
7x6 + 8x5 + 9x4 + 10x3 + 11x2 + 12x1 = 364.
You can speed this up if you notice the symmetry in the above pattern; you need only calculate the addition sum up to the sixth day (182) and then double this interim result to get 364.
You could probably speed up the calculation even more by using a formula for triangle numbers, but I couldn't find one on Wolfram Mathworld when I last looked.