Question 53
There are $40$ knights in a kingdom. Every morning they fight in pairs (everyone has exactly one enemy to fight with) and every evening they sit around a table (during the evening they do not change their seats). Find the least number of days such that:
a) the fights can be arranged in a way that every two knights have fought at least once;
b) round the table arrangements can be done in a way that every two knights have been neighbors around the table.
a) the fights can be arranged in a way that every two knights have fought at least once;
b) round the table arrangements can be done in a way that every two knights have been neighbors around the table.