How many gifts would you receive total if you received all of the gifts in the Twelve Days of Christmas?

Answer 1

The total number of gifts in the song the 12 days of Christmas is:

12+11+10+9+8+7+6+5+4+3+2+1 (subtotal=78)
+
11+10+9+8+7+6+5+4+3+2+1 (subtotal=66)
+
10+9+8+7+6+5+4+3+2+1 (subtotal=55)
+
9+8+7+6+5+4+3+2+1 (subtotal=45)
+
8+7+6+5+4+3+2+1 (subtotal=36)
+
7+6+5+4+3+2+1 (subtotal=28)
+
6+5+4+3+2+1 (subtotal=21)
+
5+4+3+2+1 (subtotal=15)
+
4+3+2+1 (subtotal=10)
+
3+2+1 (subtotal=6)
+
2+1 (subtotal=3)
+
1 (subtotal=1)
=1+3+6+10+15+21+28+36+45+55+66+78

=364
A formula for these subtotals is the sum of all the numbers from 1 to N (1 + 2 + 3 + 4 + . . . . + N) where n is each of the numbers form 1 to 12, is : (n+1)(n/2) - this formula was first worked out by Gauss.
and a formula for the sum of these sums is n(n+1)(n/2) or (n2 +n)/2

These are sometimes called the triangular numbers, because items of each of the numbers can be arranged in an equilateral (equal sided) triangle. Eg. the fifth number is 15 and 15 items can be arranged in a triangle with 5 items per side:

0
0 0
0 0 0
0 0 0 0
0 0 0 0 0

Answer 2

You would get 364 gifts.

1*12 + 2*11 + 3*10 + 4*9 + 5*8 + 6*7 + 7*6 +8*5 + 9*4 + 10*3 + 11*2 +12*1

Answer 3

The total number of gifts you would receive is 364 gifts.

Why? 1 + (1+2) + (1+2+3) + (1+2+3+4+) . . . all the way until 12.