doors.js

var Clonable = {
  clone: function(v) {
    var r = Object.create(this)
    for (var k in v) r[k] = v[k]
    return r
  }
}

Number.prototype.sqrt = function(){ 
  return Math.sqrt(this) 
}
Number.prototype.round = function(){ 
  return Math.round(this)
}
Number.prototype.eq = function(a) {
  return this.valueOf() === a.valueOf()? True : False
}

var Range = Clonable.clone({
  make(start, end) {
    return this.clone({ start: () => start, end: () => end })
  },
  start: () => 0,
  end: () => 0,
  map(f) {
    return Array.apply(null, Array((this.end() - this.start()) + 1)).map((_, i) => i + this.start())
  }
})

var True = Clonable.clone({
  thenElse(f, g){ 
    return f() 
  }
})

var False = Clonable.clone({
  thenElse(f, g){ 
    return g() 
  }
})

var Door = Clonable.clone({
  make(index){
    this.clone({ index: () => index })
  },
  isOpen(){ 
    return False
  },
  isClosed(){
    return False
  }
})

var OpenDoor = Door.clone({
  toString(){
    return "Door " + this.index().toString() + " is open."
  },
  toEmoji(){
    return "_"
  },
  isOpen(){
    return True
  }
})

var ClosedDoor = Door.clone({
  toString(){
    return "Door " + this.index().toString() + " is closed."
  },
  toEmoji(){
    return "🚪"
  },
  isClosed(){ 
    return True
  }
})

var doors = Clonable.clone({
  state(){
    Range(1, 100).map(i => 
                 (i.sqrt().eq(i.sqrt().round())).thenElse(() => OpenDoor.make(i),
                                                          () => ClosedDoor.make(i)))
  },
  open(){
    return this.state().filter(x => x.isOpen()).map(x => x.index())
  },
  closed(){
    return this.state().filter(x => x.isClosed()).map(x => x.index())
  }
})

console.log("What state are the doors in after the last pass?")
console.log(doors.state().map(x => x.toEmoji()).join(""))