Football formations are generally described by three or four nonzero whole numbers summing to 10 (the goalkeeper isn’t counted), representing, from defence to attack, the number of players in approximate lines across the pitch.

Last season we played a different formation every week, always using four lines, each with at most four players; the difference between one week and the next was that from one line two players moved, one to an adjacent line and the other to the line beyond that (eg, 3-4-1-2 could only be followed by 3-2-2-3). Our number of fixtures was the largest it could have been, given these conditions. The first number in our formations was more often 3 than any other number; 3-1-3-3 gave us our worst result.

How many games did we play, and what were our first three formations?