又一个由算24点引出的问题
先规定：只允许使用正整数范围内进行的四则运算，分步计算中只能出现正整数。开局可用的数字是1~13。问：
（1）能凑成3×8算出来的情形有多少？
（2）能凑成4×6算出来的情形有多少？
（3）能凑成2×12算出来的情形有多少？
（4）能凑成10+14算出来的情形有多少？
（5）能凑成12+12算出来的情形有多少？
（6）能算出来但不能通过以上五种方式算出来的情形有多少？ 三个字:穷举法!
四个数,24重排列,5种运算
13^4*24*5=3427320
也就340万种情况,完全可以穷举法!
穷举法万岁! 我知道穷举行得通，但我不会敲代码啊 2019-01-03 12:00
旧版没有Groupings，自己写了个递归；
2019-01-03 18:00
然后不满意默认的ToString不会调整负号为减法，又自己写了个递归。
2019-01-04 12:30
修改了等价判断依据
Array&,4]//If==1,{#},Table]]},{k,#0[#[]]}],{i,Length[#]-1}]//Flatten//Union]&//#/.(Range//Permutations//MapIndexed]]->Subscript&,#]&/@#&)&//Flatten//Union//(#~Function[{ArithmeticPermutations,DataCombinations},Parallelize]]->#1&,OneSingleData]//{#,GatherBy[#,#[]&]//(#[]//Table[\->#[],{\,#[]}]&)&/@#&//Flatten}&//Function[{RulesTypeData},Select]]==24&]//Select[#,(Level[#,{0,\}]//Which[#===a,Null,Variables[#]=={},Null,#[]===Times\#[]===-1,-#,#[]===Power\#[]===-1,#^-1,True,#]&/@#&//Complement[#,{Null}]&//#/.RulesTypeData[]&//(#\Integers\#>0)&/@#&//And@@#&)&]&//GatherBy[#,{#[],#/.RulesTypeData[]//Factor}&]&//(SortBy[#,Length]//{#[[-1]],RulesTypeData[]}&)&/@#&]]/@DataCombinations]//Join@@#&]~(Range//Tuples[#,4]&//Sort/@#&//Union))&//(Print["自然数范围内计算的"<>ToString]<>"条"];#)&//Parallelize],Subsets[#[],{0,\}]/.#[]}//If[#[]===Times,Table],x],{x,{3,4,2}}],{False,False,False}]~Join~If[#[]===Plus,Table],y],{y,{10,12}}],{False,False}]&//Append[#,Or@@#//Not]/.{True->1,False->0}&),(#//{#[]//Which[#[]===Subscript,ToString[#,InputForm],#[]===Plus,(#0/@(Select[#,Not[#[]===Times\#[]===-1]&]//If[#[]===Plus,List@@#,{#}]&)//Riffle[#,"+"]&//StringJoin)<>(Which[#1===0,"",#1[]===Plus,"-("<>#2[#1]<>")",True,"-"<>#2[#1]]&[-Select[#,#[]===Times\#[]===-1&],#0]),#[]===Times,(Table[#0//If]===Plus,"("<>#<>")",#]&,{v,Select[#,Not[#[]===Power\#[]===-1]&]//If[#[]===Times,List@@#,{#}]&}]//Riffle[#,"*"]&//StringJoin)<>(Which[#1===1,"",#1[]===Subscript,"/"<>#2[#1],True,"/("<>#2[#1]<>")"]&]===Power\#[]===-1&]^-1,#0])]&,ToString[#[],InputForm]->ToString[#[]]&/@#[]}&//StringReplace[#[],#[]]&//StringReplace[#," "->""]&)]&/@#]&//Transpose//(Do]]//ToString//{"（1）能凑成3*8算出来的情形有","（2）能凑成4*6算出来的情形有","（3）能凑成2*12算出来的情形有","（4）能凑成10+14算出来的情形有","（5）能凑成12+12算出来的情形有","（6）能算出来但不能通过以上五种方式算出来的情形有"}[]<>#&//Print,{i,6}];#[[-1]])&
自然数范围内计算的3858条
（1）能凑成3*8算出来的情形有686
（2）能凑成4*6算出来的情形有729
（3）能凑成2*12算出来的情形有716
（4）能凑成10+14算出来的情形有249
（5）能凑成12+12算出来的情形有311
（6）能算出来但不能通过以上五种方式算出来的情形有1483
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