gistfile1.txt

// JavaScript solver for http://blog.plover.com/math/17-puzzle.html

// (Cheesy yet flexible exhaustive search with recursion and eval)

var numbers = [ 6, 6, 5, 2 ];
var operators = [ '*', '/', '+', '-' ];
var goal = 17;

combine(numbers, function(numberSeries) {
  if (count(operators, numbers.length - 1, function(operatorSeries) {
    var expression = numberSeries[0].toString();
    for (var i = 0; (i < operatorSeries.length); i++) {
      expression = '(' + expression + ' ' + operatorSeries[i] + ' ' + numberSeries[i + 1].toString() + ')';
    }
    if (eval(expression) === goal) {
      console.log(expression);
      return false;
    }
  }) === false) {
    return false;
  }
});

// This works correctly if all the numbers are different, but since
// two of the numbers are the same, it will invoke iterator twice
// for each possible combination

function combine(numbers, iterator) {
  for (var i = 0; (i < numbers.length); i++) {
    var remainder = numbers.concat();
    remainder.splice(i, 1);
    if (remainder.length) {
      if (combine(remainder, function(series) {
        if (iterator([ numbers[i] ].concat(series)) === false) {
          return false;
        }
      }) === false) {
        return false;
      }
    } else {
      if (iterator([ numbers[i] ]) === false) {
        return false;
      }
    }
  }
}

// The operators need not all be used and can be used more than once.
// In other words they are digits in a number of base (number of operators).
// Just count through the possibilities. This will break like a twig
// if digits.length ^ places is greater than the largest integer
// JavaScript can represent without loss of accuracy

function count(digits, places, iterator) {
  var total = Math.pow(digits.length, places);
  var series;
  var i, j, n;
  for (i = 0; (i < total); i++) {
    n = i;
    series = [];
    for (j = 0; (j < places); j++) {
      series.push(digits[n % digits.length]);
      n = Math.floor(n / digits.length);
    }
    if (iterator(series) === false) {
      return false;
    }
  }
}