Question 1
There are two classes: class A has $m$ pupils and class B has $n$ pupils, where $m,n\gt 1$. All pupils sit around a circular table. Each pupil X receives as many candies as the number of consecutive pupils immediately to X's left belonging to the same class as X (if there are none, X receives no candy). Pupils receiving the same number of candies are placed in one group.
(a) What is the largest possible size of a group?
(b) If the group receiving no candy is excluded, what is the largest possible size of a group?
The source gives one shared 270-minute header for the two day sections. This edition applies it to each session, totaling 540 minutes; it does not claim the source prints a 540-minute annual limit or two separate timing headers. The source gives no point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
(a) What is the largest possible size of a group?
(b) If the group receiving no candy is excluded, what is the largest possible size of a group?
The source gives one shared 270-minute header for the two day sections. This edition applies it to each session, totaling 540 minutes; it does not claim the source prints a 540-minute annual limit or two separate timing headers. The source gives no point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.