2. Three sportsmen called Primus, Secundus and Tertius take part in a race every day. Primus wears the number ' 1 ' on his shirt, Secundus wears ' 2 ' and Tertius wears ' 3 '.
On Saturday Primus wins, Secundus is second and Tertius is third. Using their shirt numbers this result is recorded as ' 123 '.
On Sunday Primus starts the race in the lead with Secundus in second. During Sunday's race Primus and Secundus change places exactly 9 times, Secundus and Tertius change places exactly 10 times while Primus and Tertius change places exactly 11 times.
How will Sunday's result be recorded?
2. 231 At the start of the race, the runners are in order 123. By the end of the race Primus and Tertius have exchanged places 11 times, so Tertius ends the race ahead of Primus. Also, since Secundus and Tertius have exchanged places 10 times, Secundus ends ahead of Tertius. So the result of the race is 231 .