Solve the "Hands of Time" temporal anomaly puzzles in Final Fantasy XIII-2

hands-of-time.js

function Numbers( arr ) {
  this.numbers = arr;
  this.length = arr.length;
}

Numbers.prototype.wrapIdx = function( idx ) {
  if ( 0 <= idx && idx < this.length ) {
    return idx;
  }
  if ( idx >= this.length ) {
    return idx % this.length;
  }
  if ( idx < 0 ) {
    return idx + this.length;
  }
}

Numbers.prototype.at = function( idx ) {
  return this.numbers[ this.wrapIdx( idx ) ];
}

Numbers.prototype.next = function( idx ) {
  var currentNum = this.at( idx );
  this.numbers[ idx ] = null;

  return [
    this.wrapIdx( idx + currentNum ),
    this.wrapIdx( idx - currentNum )
  ];
};

Numbers.prototype.dupe = function() {
  return new Numbers( [].concat( this.numbers ) );
};

function test( arr ) {
  var targetLength = arr.length;
  var origNumbers = arr;

  function check( numbers, idx, idxSoFar ) {
    // console.log( numbers.numbers );
    var currentVal = numbers.at( idx );
    if ( currentVal === null ) {
      return;
    }
    var indices = [].concat( idxSoFar, idx );
    if ( indices.length === targetLength ) {
      console.log( 'did it! (' + indices.join(', ') + ')' );
      return;
    }

    var next = numbers.next( idx );
    return next.forEach(function( nextIdx ) {
      check( numbers.dupe(), nextIdx, indices );
    });
  }

  return origNumbers.map(function( val, idx ) {
    return {
      start: idx + ' (val == ' + val + ')',
      order: check( new Numbers( origNumbers ).dupe(), idx, [] )
    };
  });
}

var results = test([
  6,
  5,
  6,
  4,
  3,
  5,
  3,
  4,
  6,
  4,
  3,
  1
]);