笨人 20170402

在微信同步貼上《小學一年級算術題求解》後，有人問能否給個破解程序。我說沒問題。我用SAS和Python編程得到相同結果，但SAS比Python快很多。那就給個SAS的吧。

該小學一年級的算術題說的是：8個變量a, b, c, d, e, f, g, h, 在1到8範圍內取不同值, 求解下列4個等式中此8個變量的賦值：

1.   a+b=9

2.   c+d=7

3.   e-f=1

4.   g-h=3

下面是用SAS軟件編的蠻力破解此題的程序：

%macro DoValuation(Eq4);
data Output_&Eq4 (Keep=Variable Valuation label="Variable Valuation where g-h=&Eq4");
label Variable='Variable'
      Valuation='Valuation';
length Variable $1 Valuation s1-s8 $7;
array varArr{8} a b c d e f g h;
array lblArr{8} $1 ('a' 'b' 'c' 'd' 'e' 'f' 'g' 'h');
array strArr{8} $7 s1-s8;
do a=1 to 4;
  do b=8 to 5 by -1;
    do c=1 to 3;
          do d=6 to 4 by -1;
            do e=2 to 8;
                   do f=1 to 7;
                      do g=4 to 8;
                             do h=1 to (8 - &Eq4);
                                    AnySame=0;
                                    do i=1 to 7;
                                       do j=i+1 to 8;
                                            if varArr(i)=varArr{j}   then
                                            AnySame=1;
                                           end;
                                     end;
                                     if AnySame=0 and a+b=9 and c+d=7 and
                                       e-f=1 and g-h=&Eq4 then do i=1 to 8;
                                            if strArr(i) ne '' then  strArr(i)=cat(strip(strArr(i)),
                                            put(varArr(i),1.));
                                            else strArr(i)=put(varArr(i),1.);
                                   end;
                                  end;
                           end;
                        end;
                end;
          end;
        end;
   end;
end;
if s1 ne '' then do i=1 to 8;
    Variable=lblArr(i);
    Valuation=strip(strArr(i));
    output;
end;
run;
%mend DoValuation;

%DoValuation(3)