论坛 › 编程擂台 › 1572*8634=13572648

王守恩 发表于 2025-10-27 03:14:38

1572*8634=13572648

数码1,2恰好组成1个1位数与1个1位数。1位数×1位数=2位数。2位数恰好由数码1,2组成。有0个解。
数码1,2,3恰好组成1个1位数与1个2位数。1位数×2位数=3位数。3位数恰好由数码1,2,3组成。有0个解。
数码1,2,3,4恰好组成1个2位数与1个2位数。2位数×2位数=4位数。4位数恰好由数码1,2,3,4组成。有??个解。
数码1,2,3,4,5恰好组成1个2位数与1个3位数。2位数×3位数=5位数。5位数恰好由数码1,2,3,4,5组成。有??个解。
数码1,2,3,4,5,6恰好组成1个3位数与1个3位数。3位数×3位数=6位数。6位数恰好由数码1,2,3,4,5,6组成。有??个解。
数码1,2,3,4,5,6,7恰好组成1个3位数与1个4位数。3位数×4位数=7位数。7位数恰好由数码1,2,3,4,5,6,7组成。有??个解。
数码1,2,3,4,5,6,7,8恰好组成1个4位数与1个4位数。4位数×4位数=8位数。8位数恰好由数码1,2,3,4,5,6,7,8组成。有40个解。——譬如: 1572*8634=13572648。
数码1,2,3,4,5,6,7,8,9恰好组成1个4位数与1个5位数。4位数×5位数=9位数。9位数恰好由数码1,2,3,4,5,6,7,8,9组成。有346个解。——譬如: 1368*94257=128943576。
数码1,2,3,4,5,6,7,8,9,0恰好组成1个5位数与1个5位数。5位数×5位数=10位数。10位数恰好由数码1,2,3,4,5,6,7,8,9,0组成。有2578个解。——譬如: 10482*97653=1023598746。
数码1,2,3,4,5,6,7,8,9,0,1恰好组成1个5位数与1个6位数。5位数×6位数=11位数。11位数恰好由数码1,2,3,4,5,6,7,8,9,0,1组成。有???个解。——前面—40, 346, 2578 在慢慢长大。怎么就没有了？
数码1,2,3,4,5,6,7,8,9,0,1,2恰好组成1个6位数与1个6位数。6位数×6位数=12位数。12位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3恰好组成1个6位数与1个7位数。6位数×7位数=13位数。13位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4恰好组成1个7位数与1个7位数。7位数×7位数=14位数。14位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5恰好组成1个7位数与1个8位数。7位数×8位数=15位数。15位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6恰好组成1个8位数与1个8位数。8位数×8位数=16位数。16位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7恰好组成1个8位数与1个9位数。8位数×9位数=17位数。17位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8恰好组成1个9位数与1个9位数。9位数×9位数=18位数。18位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9恰好组成1个9位数与1个10位数。9位数×10位数=19位数。19位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0恰好组成1个10位数与1个10位数。10位数×10位数=20位数。20位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1恰好组成1个10位数与1个11位数。10位数×11位数=21位数。21位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1组成。有???个解。
数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2恰好组成1个11位数与1个11位数。11位数×11位数=22位数。22位数恰好由数码1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,8,9,0,1,2组成。有???个解。

这些解——是怎么样的一串数？谢谢！！

王守恩 发表于 2025-10-28 17:35:43

先看另外一道题。——与主帖有不同。有反例吗？谢谢！！！

数码1,1恰好组成2个1位数。1位数×1位数=2位数。2位数恰好由数码1,1组成。有"0"个解。
数码1,2,1,2恰好组成2个2位数。2位数×2位数=4位数。4位数恰好由数码1,2,1,2组成。有"0"个解。
数码1,2,3,1,2,3恰好组成2个3位数。3位数×3位数=6位数。6位数恰好由数码1,2,3,1,2,3组成。有"0"个解。
数码1,2,3,4,1,2,3,4恰好组成2个4位数。4位数×4位数=8位数。8位数恰好由数码1,2,3,4,1,2,3,4组成。有"0"个解。
数码1,2,3,4,5,1,2,3,4,5恰好组成2个5位数。5位数×5位数=10位数。10位数恰好由数码1,2,3,4,5,1,2,3,4,5组成。有"0"个解。
数码1,2,3,4,5,6,1,2,3,4,5,6恰好组成2个6位数。6位数×6位数=12位数。12位数恰好由数码1,2,3,4,5,6,,1,2,3,4,5,6组成。有"0"个解。
数码1,2,3,4,5,6,7,1,2,3,4,5,6,7恰好组成2个7位数。7位数×7位数=14位数。14位数恰好由数码1,2,3,4,5,6,7,1,2,3,4,5,6,7组成。有"0"个解。
......
用(1-n所有数的个位数)*2个数码恰好组成2个n位数。n位数×n位数=2n位数。2n位数恰好由(1-n所有数的个位数)*2个数码组成。有"0"个解。

有反例吗？谢谢！！！

王守恩 发表于 2025-10-29 05:08:55

加强一下。

n=2, 2位数=1位数×1位数。2位数,1位数与1位数分别恰好由数码1,1组成。有"0"个解。
n=3, 3位数=2位数×1位数。3位数,2位数与1位数分别恰好由数码1,2,1组成。有"0"个解。
n=4, 4位数=2位数×2位数。4位数,2位数与2位数分别恰好由数码1,2,1,2组成。有"0"个解。
n=5, 5位数=3位数×2位数。5位数,3位数与2位数分别恰好由数码1,2,3,1,2组成。有"0"个解。
n=6, 6位数=3位数×3位数。6位数,3位数与3位数分别恰好由数码1,2,3,1,2,3组成。有"0"个解。
n=7, 7位数=4位数×3位数。7位数,4位数与3位数分别恰好由数码1,2,3,4,1,2,3组成。有"0"个解。
n=8, 8位数=4位数×4位数。8位数,4位数与4位数分别恰好由数码1,2,3,4,1,2,3,4组成。有"0"个解。
n=9, 9位数=5位数×4位数。9位数,5位数与4位数分别恰好由数码1,2,3,4,5,1,2,3,4组成。有"0"个解。
n=10,10位数=5位数×5位数。10位数,5位数与5位数分别恰好由数码1,2,3,4,5,1,2,3,4,5组成。有"0"个解。
n=11,11位数=6位数×5位数。11位数,6位数与5位数分别恰好由数码1,2,3,4,5,6,1,2,3,4,5组成。有"0"个解。
n=12,12位数=6位数×6位数。12位数,6位数与6位数分别恰好由数码1,2,3,4,5,6,1,2,3,4,5,6组成。有"0"个解。
n=13,13位数=7位数×6位数。13位数,7位数与6位数分别恰好由数码1,2,3,4,5,6,7,1,2,3,4,5,6,组成。有"0"个解。

王守恩 发表于 2025-10-29 05:23:44

再加强。

对于n位数C = A × B。其中:A是a位数,B是b位数,a + b = n。

数码集合W = (1到a的个位数) + (1到b的个位数) 。

若C由数码集合W组成,A与B也由数码集合W组成。则有"0"个解。

王守恩 发表于 2025-10-30 06:53:54

1, 提炼。C = A × B。C的数码集合 = A的数码集合 + B的数码集合 = {1到a的个位数 + 1到b的个位数} 。

其中:a 是 A 的位数,b 是 B 的位数。则有"0"个解。——这个"+"没说清楚。请各位包涵。

2, 再提炼。(A × A) 的数码集合 = A 的数码集合 + A 的数码集合 。则有"0"个解。

3, 细化。C = A × B。B ≥ A。C的数码集合 = A的数码集合 + B的数码集合。A 可以是那些数？ OEIS还没有。

王守恩 发表于 2025-10-30 14:00:55

这"0"解的题目太难了。各位好友！可有反例(来一个就行)！！先丢一丢。

3×51=153。
2位数有1个。

3×501=1503。
3×510=1530。
3位数有2个。

3×4128=12384。
3×4281=12843。
3×4515=13545。
3×5001=15003。
3×5010=15030。
3×5100=15300。
3×5145=15435。
3×7125=21375。
3×7251=21753。
4位数有9个。

3×40128=120384。
3×40281=120843。
3×41028=123084。
3×41280=123840。
3×41298=123894。
3×42801=128403。
3×42810=128430。
3×42981=128943。
3×45015=135045。
3×45150=135450。
3×45618=136854。
3×47913=143739。
3×47931=143793。
3×48561=145683。
......
1位数有0个。2位数有1个。3位数有2个。4位数有9个。5位数有??个。6位数有???个。7位数有????个。——OEIS没有这串数。

northwolves 发表于 2025-10-30 14:30:03

{1,0,{}}
{2,0,{}}
{3,3,{{6,21,126},{3,51,153},{8,86,688}}}
{4,8,{{6,201,1206},{5,251,1255},{6,210,1260},{3,501,1503},{3,510,1530},{9,351,3159},{8,473,3784},{8,860,6880}}}
{5,40,{{5,2051,10255},{5,2105,10525},{9,1251,11259},{8,1481,11848},{6,2001,12006},{6,2010,12060},{3,4128,12384},{5,2501,12505},{5,2510,12550},{5,2519,12595},{6,2100,12600},{6,2127,12762},{3,4281,12843},{5,2591,12955},{3,4515,13545},{3,5001,15003},{3,5010,15030},{6,2541,15246},{3,5100,15300},{3,5145,15435},{9,1755,15795},{6,2712,16272},{2,8714,17428},{2,8741,17482},{3,7125,21375},{3,7251,21753},{5,5021,25105},{5,5102,25510},{9,3501,31509},{9,3510,31590},{8,4730,37840},{8,4973,39784},{6,7446,44676},{9,5751,51759},{8,6521,52168},{9,6255,56295},{9,7461,67149},{8,8600,68800},{9,7911,71199},{9,8775,78975}}}
{6,195,{{5,20051,100255},{5,20105,100525},{5,20501,102505},{5,20510,102550},{5,20519,102595},{5,20591,102955},{8,13046,104368},{5,21005,105025},{5,21050,105250},{5,21059,105295},{6,18021,108126},{6,18102,108612},{5,21905,109525},{9,12501,112509},{9,12510,112590},{6,19416,116496},{8,14801,118408},{8,14810,118480},{6,19821,118926},{8,14981,119848},{6,20001,120006},{6,20010,120060},{3,40128,120384},{6,20100,120600},{6,20127,120762},{3,40281,120843},{6,20181,121086},{3,41028,123084},{3,41280,123840},{3,41298,123894},{5,25001,125005},{5,25010,125050},{5,25019,125095},{5,25100,125500},{5,25190,125950},{5,25199,125995},{6,21000,126000},{6,21018,126108},{6,21270,127620},{3,42801,128403},{3,42810,128430},{3,42981,128943},{9,14382,129438},{5,25901,129505},{5,25910,129550},{6,21594,129564},{5,25919,129595},{5,25991,129955},{5,26513,132565},{5,26531,132655},{3,45015,135045},{3,45150,135450},{3,45618,136854},{8,17348,138784},{2,71489,142978},{3,47913,143739},{3,47931,143793},{3,48561,145683},{2,74891,149782},{3,50001,150003},{3,50010,150030},{6,25041,150246},{3,50100,150300},{3,50145,150435},{6,25104,150624},{6,25401,152406},{6,25410,152460},{6,25491,152946},{3,51000,153000},{3,51450,154350},{5,31265,156325},{9,17550,157950},{6,27012,162072},{6,27120,162720},{5,32651,163255},{3,54618,163854},{3,54861,164583},{8,20651,165208},{8,21065,168520},{6,28731,172386},{2,87014,174028},{2,87041,174082},{2,87104,174208},{2,87140,174280},{2,87149,174298},{2,87401,174802},{2,87410,174820},{2,87491,174982},{2,89147,178294},{2,89471,178942},{2,89714,179428},{2,89741,179482},{2,91487,182974},{9,20781,187029},{9,21078,189702},{2,94871,189742},{9,21375,192375},{2,98714,197428},{2,98741,197482},{3,70125,210375},{3,70251,210753},{3,71025,213075},{3,71250,213750},{9,23751,213759},{3,72501,217503},{3,72510,217530},{9,25731,231579},{9,26325,236925},{6,39828,238968},{6,40251,241506},{6,41025,246150},{5,50021,250105},{5,50102,250510},{5,50201,251005},{5,50210,251050},{5,50219,251095},{5,51002,255010},{5,51020,255100},{5,51263,256315},{9,28755,258795},{5,51902,259510},{3,87126,261378},{3,87261,261783},{5,52631,263155},{8,35672,285376},{6,47829,286974},{6,48279,289674},{3,97125,291375},{3,97251,291753},{9,32625,293625},{5,59021,295105},{5,59102,295510},{8,37229,297832},{5,62513,312565},{5,62531,312655},{9,34911,314199},{9,35001,315009},{9,35010,315090},{5,63125,315625},{9,35100,315900},{5,63251,316255},{5,65123,325615},{5,65231,326155},{8,42836,342688},{8,43286,346288},{9,39555,355995},{8,46013,368104},{8,46733,373864},{8,47300,378400},{9,42381,381429},{9,43713,393417},{9,43875,394875},{8,49730,397840},{8,49973,399784},{9,46251,416259},{8,54473,435784},{6,74460,446760},{6,74496,446976},{6,74946,449676},{8,56471,451768},{8,57146,457168},{6,79482,476892},{9,54288,488592},{6,81948,491688},{9,54873,493857},{6,82947,497682},{9,57501,517509},{9,57510,517590},{8,65021,520168},{8,65102,520816},{8,65201,521608},{8,65210,521680},{9,62550,562950},{6,94152,564912},{8,71456,571648},{8,77216,617728},{9,68751,618759},{8,82661,661288},{9,74601,671409},{9,74610,671490},{8,86000,688000},{9,78021,702189},{9,78102,702918},{9,79011,711099},{9,79101,711909},{9,79110,711990},{9,79551,715959},{9,79911,719199},{8,92741,741928},{8,96737,773896},{8,97367,778936},{8,97862,782896},{9,87255,785295},{9,87750,789750},{9,87921,791289}}}

northwolves 发表于 2025-10-30 14:31:17

For==0,x=y/k;a=SortBy,{k}]],First];b=SortBy],First];If]]]];Print[{n,Length@s,s}]]

northwolves 发表于 2025-10-30 14:39:39

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northwolves 发表于 2025-10-30 15:25:05

本帖最后由 northwolves 于 2025-10-30 16:10 编辑

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