有10根竹籤分別為 1公分2公分3公分4公分5公分6公分7公分8公分9公分10公分 想要每次取三根排三角形 Q.總共可以排出幾個?(請詳列)?

(10,9,8),(10,9,7),(10,9,6),(10,9,5),(10,9,4),(10,9,3),(10,9,2),
(10,8,7),(10,8,6),(10,8,5),(10,8,4),(10,8,3),
(10,7,6),(10,7,5),(10,7,4),
(10,6,5);

(9,8,7),(9,8,6),(9,8,5),(9,8,4),(9,8,3),(9,8,2),
(9,7,6),(9,7,5),(9,7,4),(9,7,3),
(9,6,5),(9,6,4);

(8,7,6),(8,7,5),(8,7,4),(8,7,3),(8,7,2),
(8,6,5),(8,6,4),(8,6,3),
(8,5,4);

(7,6,5),(7,6,4),(7,6,3),(7,6,2),
(7,5,4),(7,5,3);

(6,5,4),(6,5,3),(6,5,2),
(6,4,3);

(5,4,3),(5,4,2);

(4,3,2)

總共可以排出 (7+5+3+1) + (6+4+2) + (5+3+1) + (4+2) + (3+1) + (2) + (1)
= (7+6+5+4+3+2+1) + (5+4+3+2+1) + (3+2+1) + (1)
= 28 + 15 + 6 + 1
= 50個三角形。