cinelli wrote:Eight athletes took part in a recent sporting competition which comprised several events. The final standings were as follows:
How many events were there in the competition and how were the points awarded?
Something missing there, I think, otherwise there are huge numbers of solutions, such as:
* 984 events, each event awarded 1 point to the winner and none to anyone else, each athlete won the indicated number of events.
* 492 events, each event awarded 2 points to the winner and none to anyone else, each athlete won half the indicated number of events.
* 2 events, awarding 224, 120, 56, 35, 27, 20, 9 and 1 points for 1st-8th places, the athletes came in the same order in both events.
Of course, 984 and 492 are rather larger than what people tend to mean by "several", and 2 rather smaller, so the intended answer might involve the number of events being in the right range to count as "several". But different people have different ideas about just what that range is, so if that's the case, an explicit range ought to be stated...
Other information that might be missing includes whether each event awarded points in the same way, whether points only depend on the athlete's position or depend in some way on their exact performance (competitions such as the heptathlon do the latter), and whether points from different events are combined by adding them together or might be combined in some other fashion (e.g. by multiplying them together).