规律是:三个数都是3的倍数
有这样的共96个算式:
246+789=1035,249+786=1035,264+789=1053,269+784=1053,284+769=1053
286+749=1035,289+746=1035,289+764=1053,324+765=1089,325+764=1089
342+756=1098,346+752=1098,347+859=1206,349+857=1206,352+746=1098
356+742=1098,357+849=1206,359+847=1206,364+725=1089,365+724=1089
423+675=1098,425+673=1098,426+879=1305,429+876=1305,432+657=1089
437+589=1026,437+652=1089,439+587=1026,452+637=1089,457+632=1089
473+589=1062,473+625=1098,475+623=1098,476+829=1305,479+583=1062
479+826=1305,483+579=1062,487+539=1026,489+537=1026,489+573=1062
537+489=1026,539+487=1026,573+489=1062,579+483=1062,583+479=1062
587+439=1026,589+437=1026,589+473=1062,623+475=1098,624+879=1503
625+473=1098,629+874=1503,632+457=1089,637+452=1089,652+437=1089
657+432=1089,673+425=1098,674+829=1503,675+423=1098,679+824=1503
724+365=1089,725+364=1089,742+356=1098,743+859=1602,746+289=1035
746+352=1098,749+286=1035,749+853=1602,752+346=1098,753+849=1602
756+342=1098,759+843=1602,764+289=1053,764+325=1089,765+324=1089
769+284=1053,784+269=1053,786+249=1035,789+246=1035,789+264=1053
824+679=1503,826+479=1305,829+476=1305,829+674=1503,843+759=1602
847+359=1206,849+357=1206,849+753=1602,853+749=1602,857+349=1206
859+347=1206,859+743=1602,874+629=1503,876+429=1305,879+426=1305
879+624=1503
具体分析如下:
因为"两个数相加等于第三个数,且十个数字必须用且只可用一次",所以只能是两个三位数相加等于一个四位数,该四位数的千位上的数字只能是1.再根据加法进位原理,最终可确定该四位数只
能是1206、1035、1503、1062、1089、1098、1206、1305、1503、1602,当四位数是1053或者1089或者1098有成立的三个数各有16个:(324,765,1089),(342,756,1098),...(346,752,1098),
(364,725,1089),(724,365,1089),(423,675,1098).(其它的可类似写出:对前两个数交换个位,交换十位,交换百位)当四位数是1206有成立的三个数10个:(359,847,1206),
(349,857,1026),(847,359,1026),(357,849,1026).当四位数是1035或者1062或者1305或者1602有成立的三个数各有8个,用相同的道理可以推出.
487+539=1026,489+537=1026,537+489=1026,539+487=1026,587+439=1026,589+437=1026 (6)
246+789=1035,249+786=1035,286+749=1035,289+746=1035,746+289=1035,749+286=1035,786+249=1035,789+246=1035 (8)
264+789=1053,269+784=1053,284+769=1053 ,289+764=1053,769+284=1053,764+289=1053,784+269=1053,789+264=1053,824+679=1503,874+629=1503,624+879=1503,629+874=1503,
674+829=1503,679+824=1503 ,829+674=1503,879+624=1503 (16)
473+589=1062,479+583=1062,483+579=1062,573+489=1062,579+483=1062,583+479=1062 ,489+573=1062 ,589+473=1062 (8)
324+765=1089,325+764=1089 ,364+725=1089,365+724=1089,432+657=1089,437+652=1089,452+637=1089,457+632=1089,632+457=1089,637+452=1089,652+437=1089,657+432=1089,
724+365=1089,725+364=1089,764+325=1089,765+324=1089 (16)
342+756=1098,346+752=1098,352+746=1098 ,356+742=1098,423+675=1098,425+673=1098,473+625=1098,475+623=1098,623+475=1098,625+473=1098,673+425=1098,675+423=1098
742+356=1098,746+352=1098,752+346=1098,756+342=1098 (16)
347+859=1206,349+857=1206,357+849=1206,359+847=1206,437+589=1026,439+587=1026,847+359=1206,849+357=1206,857+349=1206 ,859+347=1206 (10)
426+879=1305,429+876=1305,476+829=1305,479+826=1305,826+479=1305,829+476=1305,876+429=1305,879+426=1305 (8)
743+859=1602,749+853=1602,753+849=1602 ,759+843=1602,843+759=1602 ,849+753=1602,853+749=1602,859+743=1602 (8)