MathDB

In a soccer tournament between four teams,

A

B

C

, and

D

, each team plays each of the others exactly once. a) Decide if, at the end of the tournament, it is possible for the quantities of goals scored and goals allowed for each team to be as follows: \begin{tabular}{ c|c|c|c|c } {} & A & B & C & D \\ \hline Goals scored & 1 & 3 & 6 & 7 \\ \hline Goals allowed & 4 & 4 & 4 & 5 \\ \end{tabular} If the answer is yes, give an example for the results of the six games; in the contrary, justify your answer. b) Decide if, at the end of the tournament, it is possible for the quantities of goals scored and goals allowed for each team to be as follows: \begin{tabular}{ c|c|c|c|c } {} & A & B & C & D \\ \hline Goals scored & 1 & 3 & 6 & 13 \\ \hline Goals allowed & 4 & 4 & 4 & 11 \\ \end{tabular} If the answer is yes, give an example for the results of the six games; in the contrary, justify your answer.

Problem Statement