Okay, this is a math question in the form of Naruto. It is a very challening question despite that. I'm interested to see if anyone can solve it. Do not ask for the answer, I will not give it to you until someone gets the right answer and I don't give hints.
Iruka devised a way to train the ninja academy students in the art of mass combat. These mock battles are divided into 2 rounds. Round A and Round B.
Round A : The students are allowed to fight against anyone and as many opponents they choose. (i.e. 1 nin can go against 5, or 3 can go against 7) However, the nins cannot change opponents.
Round B : The students must not spar with the opponents encounted in the previous round and must spar with all those they didn't fight in the first round.
This is to ensure that the weakest student will have a chance to fight the strongest of the lot and that the ninja-wannabes will be trained in fighting as a part of a group or against many. Each student is tagged numerically and Iruka draws up a table that lists the opponents of each student.
Question: In one particular battle, Iruka discovered that the table he gets in the 2nd round could be made identical to that in the 1st round simply by re-labelling the students. If all the students are now divided into squads of 4, what is the possible numbers of students that will be left over?
Iruka devised a way to train the ninja academy students in the art of mass combat. These mock battles are divided into 2 rounds. Round A and Round B.
Round A : The students are allowed to fight against anyone and as many opponents they choose. (i.e. 1 nin can go against 5, or 3 can go against 7) However, the nins cannot change opponents.
Round B : The students must not spar with the opponents encounted in the previous round and must spar with all those they didn't fight in the first round.
This is to ensure that the weakest student will have a chance to fight the strongest of the lot and that the ninja-wannabes will be trained in fighting as a part of a group or against many. Each student is tagged numerically and Iruka draws up a table that lists the opponents of each student.
Question: In one particular battle, Iruka discovered that the table he gets in the 2nd round could be made identical to that in the 1st round simply by re-labelling the students. If all the students are now divided into squads of 4, what is the possible numbers of students that will be left over?
