Answer
78
Work Step by Step
The number of gifts daily form a sequence
$1$,
$1+2$,
$1+2+3$,
$1+2+3+4$,
$\cdots$,
$1+2+3+...+12$
On the n-th day the number of gifts increases ny n.
Forming a sequence of increases in gifts, we obtain
1, 2, 3, 4, ... 11, 12,...
which is an arithmetic sequence with $a=1$ and $d=1$
The number of gifts on the 12th day is the sum of the first 12 terms of this sequence (12th partial sum of the arithmetic sequence).
The sum is
$S_{n}=\displaystyle \frac{n}{2}[2a+(n-1)d]$
$S_{12}=12(\displaystyle \frac{1+12}{2})$
$=6\cdot 13$
$=78$
