The FIFA world cup draw is occurring this week, with the teams in the draw as shown below. 8 groups will be selected, containing 1 team from each pot. The colours represent the continent. No continent other than Europe (pale blue) can have more than one team in each group, Europe being able to have no more than 2. The numbers in brackets are the country rankings, the lower number being a better team.
Abiding by these rules, what is the (positive integer) difference between the total rankings of the best and worst possible groups that England could be in?
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It is clear that England's worst ranked group should contain Russia. Despite the limitations on the number of teems from each continent, they are much worse ranked than any other team in pot 1. Pot 2 will obviously contain England. From pot 3, the worst teams possible are Senegal and Iran. If Iran were in it, it would mean that the worst team from pot 4 available would be Panama. However, this has a lower score than Senegal and Saudi Arabia.
In England's best ranked group (which would be the worst for England!), there can be only one other European team. This table shows the teams that could be chosen from each pot, with the Europeans in italics .
None of Brazil, Costa Rica or Nigeria are from the same continent as each other, meaning that these 6 teams are the only ones that need contemplating. Also, as the Europeans have the best rankings in their respective groups, to minimise the number, we should pick one from Europe, and two of Brazil, Costa Rica and Nigeria.
Germany + Costa Rica + Nigeria = 6 4
Denmark + Brazil + Nigeria = 6 2
Serbia + Brazil + Costa Rica = 6 2
It does not matter which of these two groups that England are with, the ranking is the same. Hence,
( Russia + England + Senegal + Saudi Arabia ) − ( Brazil + England + Denmark + Nigeria ) = 1 7 2 − 7 4 = 9 8