DouKaku?

import scala.util.parsing.combinator.{Parsers, ImplicitConversions, ~, mkTilde}
import scala.util.parsing.combinator.syntactical.StdTokenParsers
import scala.util.parsing.combinator.lexical.StdLexical

object Komachi extends StdTokenParsers with Application{
  type Tokens = StdLexical ; val lexical = new StdLexical
  lexical.delimiters ++= List("+","-", "*", "/")
  def expr = term*("+" ^^ {(x: double, y: double) => x + y}
                 | "-" ^^ {(x: double, y: double) => x - y})
  def term = factor*("*" ^^ {(x: double, y: double) => x * y}
                   | "/" ^^ {(x: double, y: double) => x / y})
  def factor: Parser[double] = numericLit ^^ (_.toDouble)

  ((List(List[String]())) /: List.make(8, List("+", "-", "*", "/", ""))){
    for(i <-_; j <-_) yield j::i
  }.foreach{fs =>
    val s = (new StringBuilder("1") /: (2 to 9)){(s,i) =>
      s.append(fs(i-2)).append(i)
    }.toString
    if(expr(new lexical.Scanner(s)).get == 100.0) println(s)
  }
}