19. (6 points) There are several small sticks of lengths 1 cm, 2 cm, 3 cm, 4 cm, and 5 cm each. If you randomly pick 3 sticks to form a triangle, what is the maximum number of different triangles that can be formed?
【Answer】Solution: (1) 1 cm, 1 cm, 1 cm;
(2) 1 cm, 2 cm, 2 cm;
(3) 1 cm, 3 cm, 3 cm;
(4) 1 cm, 4 cm, 4 cm;
(5) 1 cm, 5 cm, 5 cm;
(6) 5 cm, 5 cm, 5 cm;
(7) 2 cm, 2 cm, 2 cm;
(8) 2 cm, 2 cm, 3 cm;
(9) 2 cm, 3 cm, 3 cm;
(10) 2 cm, 3 cm, 4 cm;
(11) 2 cm, 4 cm, 4 cm;
(12) 2 cm, 4 cm, 5 cm;
(13) 2 cm, 5 cm, 5 cm;
(14) 3 cm, 3 cm, 3 cm;
(15) 3 cm, 3 cm, 4 cm;
(16) 3 cm, 3 cm, 5 cm;
(17) 3 cm, 4 cm, 4 cm;
(18) 3 cm, 4 cm, 5 cm;
(19) 3 cm, 5 cm, 5 cm;
(20) 4 cm, 4 cm, 4 cm;
(21) 4 cm, 4 cm, 5 cm;
(22) 4 cm, 5 cm, 5 cm.

Answer: A maximum of 22 different triangles can be formed.