因为在1、2、3、4、5这五个数里，1+2+3=6,3+4+5=12,1+3+5=9中6、12、9都能被3整除。
所以，由1,2,3,4,5这五个数字能组成没有重复数字的被3整除的三位数有：123、132、213、231、312、321、345、354、435、453、534、543、135、153、315、351、513、531共18个。
3,12,15,21,24,42,45,51,123,132,135,153,213,231,243,234,312,321,345,354,315,351,423,432,513,531,1245,1254,1425,1452,1524,1542,2154,2145,2451,，2415,2514,2541,12345,12354,12435,12453,12534,12543,13245,13254,13425,13452,13542,13524,14235,14253,14325,14352,14523,14532,15234,15243,15324,15342,15423,15432,21345,21354,21435,21453,21543,21534,23145,23154,23415,23451,23541,23514,,24135,24153,24315,24153,24513,24531,31245,31254,31452,31425,31524,31542,32145,32154,32415,23451,32514,32541,34125,34152,34215,34251,34512,34521,35124,35142,35214,35241,35412,35421,41235,41253,41325,41352,41523,41532,42125,42153,42315,42351,42513,42531,43125,43152,43215,43251,43512,43521,45123,45132,45213,45231,45312,45321,51234,51243,,51324,51342,51423,51432,52134,52143,52314,52341,52431,52413,53124,53142,53214,53241,53421,53412,54123,54132,54231,54213,54321,54312
啊啊啊，太多了。
总共这些。好像152个数。
如果说是N位数，那N个数之和被三整除，那这个数可以被三整除,可以自己试。
望采纳谢谢。 （累死了，一定要选满意呦~~~~）
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