A few years ago, a well known laundry detergent manufacturer ran a sales-promotion competition in Australia called “Jack-in-the-box”, with the following rules:

1. 1. Draw a continuous line through 13 of the numbered squares (see Fig. 1). The numbers in the squares through which the line has been drawn are then added to give a total score. Entries achieving the highest total scores will qualify for one of the prizes.

2. 2. The line must not go through any square more than once. It also cannot be drawn diagonally through the corner of any squares_only up and down or across (see the example in Fig. 1, for which the score is 723).

3. 3. The line must begin at the square J (for Jack-in-the-box) and may finish in any square. The J square does not count as one of the 13 squares.