A maths puzzle

[DaveReading]

A competition is held between 50 teams, each team competing in the same seven events.

For each event, teams are ranked based on results, from 1st to 50th (equal placings are possible).

A team's rankings for each event are combined as a weighted sum: Events 1-4 are weighted at 50%, Events 5-6 at 150% and Event 7 at 60%. So, for example, 3 places higher in Event 1 would cancel out one place lower in Event 5.

A team that achieves 7 first places is awarded 1000 points. A team that achieves 7 50th places gets zero points.

How many points (rounded to the nearest whole number) would a team be awarded it its rankings for the seven events were, respectively:

a) 1st, 8th, 1st, 46th, 3rd, 13th and 34th

b) 10th, 15th, 15th, 42nd, 23rd, 7th and 36th

 

[Drago]

Three.

One.

 

[Beebo]

 

[Pro Tour Punditry]

If it doesn't involve Burgers and chips it's not a proper modern day maths test

 

[Markymark]

If it doesn't involve Burgers and chips it's not a proper modern day maths test

Or a proper Scottish breakfast.

 

[Levo-Lon]

Sunday..that's got to be right

 

[PK99]

41

 

[raleighnut]

41

42 surely.

 

[DaveReading]

42 surely.

Well I did ask for two answers, so you could both be right.

But, sadly, you aren't.

 

[nickyboy]

At the risk of taking this rather too seriously...

You've not supplied sufficient information to calculate the answer. You've said that if a team comes 1st they get a lot of points and if the come 50th they get no points. But you haven't said whether the relationship between placing and points is linear or not (ie if they come second do they get 49/50 of what they would have got if they had come first). Without that it's impossible to answer

 

[Tin Pot]

A competition is held between 50 teams, each team competing in the same seven events.

For each event, teams are ranked based on results, from 1st to 50th (equal placings are possible).

A team's rankings for each event are combined as a weighted sum: Events 1-4 are weighted at 50%, Events 5-6 at 150% and Event 7 at 60%. So, for example, 3 places higher in Event 1 would cancel out one place lower in Event 5.

A team that achieves 7 first places is awarded 1000 points. A team that achieves 7 50th places gets zero points.

How many points (rounded to the nearest whole number) would a team be awarded it its rankings for the seven events were, respectively:

a) 1st, 8th, 1st, 46th, 3rd, 13th and 34th

b) 10th, 15th, 15th, 42nd, 23rd, 7th and 36th

As @nickyboy points out and assuming 20pts per placing..

a)The sum of
1000*0.5
840*0.5
1000*0.5
80*0.5
960*1.5
740*1.5
320*0.6

b) The same methodology

However, the nature of your question leads me to believe there is something behind this you are not sharing with us. For example, you mention that placing maybe equal, but this isn't called for in the question. Is this a real world ranking?

 

[DaveReading]

At the risk of taking this rather too seriously...

You've not supplied sufficient information to calculate the answer. You've said that if a team comes 1st they get a lot of points and if the come 50th they get no points. But you haven't said whether the relationship between placing and points is linear or not (ie if they come second do they get 49/50 of what they would have got if they had come first). Without that it's impossible to answer

Sorry, I thought I'd implied that in my description of the problem.

But yes, the points gap between a team that gets 7 first places and one that gets 7 second places would be the same as between a team with all 49ths and a team with all 50ths (in both cases a difference of 1000/49 i.e. roughly 20.4).

 

[DaveReading]

As @nickyboy points out and assuming 20pts per placing..

a)The sum of
1000*0.5
840*0.5
1000*0.5
80*0.5
960*1.5
740*1.5
320*0.6

But that adds up to way more than the 1000 points that a team with seven firsts would score.

And yes, it's a real-world problem (albeit slightly disguised, but the numbers are the same).

 

[Tin Pot]

But that adds up to way more than the 1000 points that a team with seven firsts would score.

And yes, it's a real-world problem (albeit slightly disguised, but the numbers are the same).

Does it? I don't think so.

Unless you only give points at the end, and this is a ranking problem?

 

[DaveReading]

Does it? I don't think so.

Unless you only give points at the end, and this is a ranking problem?

The points are derived solely from the rankings in the seven individual events, using the weighting I quoted, and the maximum/minimum values of 1000 and zero.

I'm concerned that there appears to be ambiguity in my description of the problem, but I'm having trouble seeing where it is. Help welcomed.