Song competition - ranking order and breaking ties

Hi,

We run a song competition where periodically songs are scored out of ten by four judges.

The top six songs then move on to the next stage.

Inevitably there are ties. To break them I use a manual method which involves looking at the sum of the highest three votes for the songs, eg 7,6,6 would win over 7,6,5.

Sometimes this doesn't work as a straightforward sum eg. 5,5,4 = 14, 6,4,4 = 14. In this case I would say that 6,4,4 wins because 6 is higher than 5.

I've been trying to automate this tie-breaking process in a spreadsheet but really it's beyond my capabilities! I've attached it in case anyone wanted to have a look and suggest a possible formula.

As you'll see, I have a 'places' column where I've used the RANK operator to generate places from 1 to 12. This is of limited use because of the ties.
There are four ties on the spreadsheet, each involving two songs at 17, 18, 22 and 27 points. The ties are highlighted in cream.

It's probably too much to ask that all of these ties can be broken by a formula but it's worth a try. Ideally I want to end up with a ranking column with the songs' positions from 1-12.

Many thanks in advance.

PS The pale blue fill is a conditional format to highlight the top six songs.