三角形组合

来源:百度知道 编辑:UC知道 时间:2024/05/12 08:47:05
已知有足够多的1厘米,2厘米,3厘米,4厘米,5厘米,6厘米,7厘米,8厘米,9厘米,10厘米和11厘米长的小木条,可以组成多少个三角形框架?
(请详细帮助解答)

111,122,133,144,155,166,177,188,199,1(10)(10),1(11)(11)计:1×11=11种
222,223,233,234,244,245,255,256,266,267,277,278,288,289,299,29(10),2(10)(10),2(10)(11),2(11)(11)计:2×9+1=19种
333,334,335,344,345,346,355,356,357,366,367,368,377,378,379,388,389,38(10),399,39(10),39(11),3(10)(10),3(10)(11),3(11)(11)计:3×7+2+1=24种
444,445,446,447,455,456,457,458,466,467,468,469,477,478,479,47(10),488,489,48(10),48(11),499,49(10),49(11),4(10)(10),4(10)(11),4(11)(11)计:4×5+3+2+1=26种
555,556,557,558,559,566,567,568,569,56(10),577,578,579,57(10),57(11),588,589,58(10),58(11),599,59(10),59(11),5(10)(10),5(10)(11),5(11)(11)计:5×3+4+3+2+1=25种
666,667,668,669,66(10),66(11),677,678,679,67(10),67(11),688,689,68(10),68(11),699,69(10),69(11),6(10)(10),6(10)(11),6(11)(11)计:6×1+5+4+3+2+1=21种
777,778,779,77(10),77(11),788,789,78(10),78(11),799,79(10),79(11),7(10)(10),7(10)(11),7(11)(11)计:5+4+3+2+1=15种
888,889,88(10),88(11),899,89(10),89(11),8(10)(10),8(10)(11),8(11)(11)计:4+3+2+1=10种