fcn toInt(digits,remove_digit=0){
   if(remove_digit!=0) digits=digits.copy().del(digits.index(remove_digit));
   digits.reduce(fcn(s,d){ s*10 + d });
}
fcn nDigits(n){
    //-- generate numbers with unique digits efficiently
    //-- and store them in an array for multiple re-use,
    //-- along with an array of the removed-digit values.
    res,digits := List(), n.pump(List(),'+(1));  // 1,2,3,4..n
    used       := List.createLong(n,1).extend(List.createLong(9-n,0));
    while(True){
       nine:=List.createLong(9,0);
       foreach i in (used.len()){ if(used[i]) nine[i]=toInt(digits,i+1) }
       res.append(T(toInt(digits),nine));
       found:=False;
       foreach i in ([n-1..0, -1]){
          d:=digits[i];
    if(not used[d-1]) println("ack!");
    used[d-1]=0;
    foreach j in ([d..8]){
       if(not used[j]){
    used[j]=1;
    digits[i]=j+1;
    foreach k in ([i+1..n-1]){
       digits[k] = used.find(0) + 1;
       used[digits[k] - 1]=1;
    }
    found=True;
    break;
       }
    }
    if(found) break;
       }//foreach i
       if(not found) break;
    }//while
    res
}

foreach n in ([2..5]){
   rs,rsz,count,omitted := nDigits(n),rs.len()-1, 0, List.createLong(9,0);
   foreach i in (rsz){
      xn,rn := rs[i];
      foreach j in ([i+1..rsz]){
         xd,rd := rs[j];
   foreach k in ([0..8]){
      yn,yd := rn[k],rd[k];
      if(yn!=0 and yd!=0 and
           xn.toFloat()/xd.toFloat() == yn.toFloat()/yd.toFloat()){
         count+=1;
         omitted[k]+=1;
         if(count<=12)
      println("%d/%d --> %d/%d (removed %d)".fmt(xn,xd,yn,yd,k+1));
      }
   }
      }
   }
   println("%d-digit fractions found: %d, omitted %s\n"
      .fmt(n,count,omitted.concat(",")));
}