game problem?

Question: here is a problem with detailed solution. http://docs.google.com/Doc?id=dc83hzcs_161g58shg I don't understand some part of the solution. I have made red marks over there. please clarify

Answer: I don't think there is a need to start with South Africa first. What it appears they did was start with the 3 countries between Australia and Canada and set up 3 unknowns (essentially at the same time). The reason for this is there is an explicit upper and lower bound in their total points (i.e. between 19 and 24 points). Instead for New Zealand there is only an implicit lower bound which needs to be determined first. Of these 3 it makes more sense to start with South Africa or England than Scotland for the same reason. ================ South Africa has 2 gold and 5 bronze. There is only 1 unknown (silver) - call it x. 2 gold and 5 bronze is worth 2*3+5=11 points. Silvers are worth 2 each. South Africa must have won at least 5 silver (x=5) since that is the fewest silvers they can have that would give them more points than Canada 11+2x>19 and x=4 -> 11+8=19 and x=5 -> 11+10=21 Recall that since Canada has more gold, South Africa would lose the tie breaker if they had the same total points thus they must have more to be ranked higher. So South Africa must have at least 5 silver meaning they would have at least 21 points. If they won 6 silver they would have 23 points which is feasible. They can't have won 7 silver since that would give them 25 points and they cannot have more points than Australia who is ranked first! So x=4 or x=5. ================ Was that all you needed help with?

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