【Question 13】
There are 91 sticks, with lengths of $1 \mathrm{~cm}, 2 \mathrm{~cm}, 3 \mathrm{~cm}, 4 \mathrm{~cm}, \cdots, 91 \mathrm{~cm}$, respectively. At least $\qquad$ sticks need to be selected to ensure that a triangle can definitely be formed.
【Analysis and Solution】
The worst-case principle.
To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
On one hand, assume there exist 8 sticks that cannot form a triangle;
The 3rd smallest number is no less than $1+2=3$,
The 4th smallest number is no less than $1+2+3=6$,
The 5th smallest number is no less than $1+2+3+6=12$,
The 6th smallest number is no less than $1+2+3+6+12=24$,
The 7th smallest number is no less than $1+2+3+6+12+24=48$,
The 8th smallest number is no less than $1+2+3+6+12+24+48=96$,
This contradicts the condition that the longest stick is no more than 91;
Therefore, the original assumption is invalid, meaning that any 8 sticks selected can form a triangle.
On the other hand, sticks with lengths of $1,2,3,6,12,24,48$ cannot form a triangle.
In summary, selecting at least 8 sticks will definitely allow the formation of a triangle.