Question 25
At the 2018 FIFA World Cup, 32 teams were divided into eight groups A, B, C, D, E, F, G and H of four teams each. In the first round each pair of teams in a group played one match. A winner received 3 points and a loser 0; in a draw each team received 1 point. After the first round, the two highest-scoring teams in each group advanced to the second round.
If the answer is not an integer, give the nearest integer. If the calculated answer has more than five digits, give its last five digits.
After the first round there are $m$ drawn matches. The group totals are shown: A: $n+3$; B: $n$; C: $n+1$; D: $n+2$; E: $n+1$; F: $n+3$; G: $n+3$; H: $n+2$. For positive integers $m,n$, find the sum of all possible values of $m$.
If the answer is not an integer, give the nearest integer. If the calculated answer has more than five digits, give its last five digits.
After the first round there are $m$ drawn matches. The group totals are shown: A: $n+3$; B: $n$; C: $n+1$; D: $n+2$; E: $n+1$; F: $n+3$; G: $n+3$; H: $n+2$. For positive integers $m,n$, find the sum of all possible values of $m$.