Maths Homework For An 11 Year Old

[Shutpa]

Sam had never fully understood the points system in football and felt that the scoring of goals should be encouraged. His idea was that 10 points should be awarded for a win, 5 points for a draw and 1 point for each goal scored, whatever the result of the match. Therefore even if you are losing 0-5 and have no hope of winning, a goal scored might make all the difference between promotion and relegation. This was tried with three teams, Hubs, Dins and Rungs. Each team scored at least one goal in every match and no team played another more than once. Hubs scored 8 points, Dins 14 points and Rungs 9 points. Find the score of each match.

Any good at maths?

 

[Rob]

Not possible.

 

[Shutpa]

Not possible.

Thats what I thought. I wonder what the teacher will come up with?

 

[sooey]

Assuming that each team played two games, I agree with Rob, it doesn't work out.

 

[Rob]

They couldnt have all drew with each other.
If one team WON that means they LOST another. To who.

 

[Softus]

Hubs scored 8 points, Dins 14 points and Rungs 9 points.

As rob884 has already pointed out, that permutation of scores is not possible with the points system that you've defined.

 

[mobileman]

The only way that works out is if Rungs played two games and Dins and Hubs only played one game. It doesn't say in the question that they DID play two games each, just that they DIDN'T play the same team twice.

Therefore:

RUNGS 1 - DINS 4
RUNGS 3 - HUBS 3

 

[Softus]

The only way that works out is if Rungs played two games and Dins and Hubs only played one game.

Good point!

However, that wouldn't be football.

 

[tim west]

Sam had never fully understood the points system in football

This suggests that Sam's system is therefore flawed and the results given cannot be used for analysis and the giving of any answer to the question.

 

[mobileman]

Good point!

However, that wouldn't be football.

You're right, it ain't football - it's maths. They want kids to try and think outside of the box. Wasn't like that when I as a kid I tell ya!

 

[Trazor]

Assuming the teams played each other once...

3 draws of 1-1 .............................= 36 points
1 win.........2-1 and 2 draws.... 1-1 = 37 points
2 wins.......2-1 and 1 draw......1-1 = 38 points
3 wins.......2-1.............................= 39 points

The lowest total scores possible.

 

[mobileman]

Sam had never fully understood the points system in football

This suggests that Sam's system is therefore flawed and the results given cannot be used for analysis and the giving of any answer to the question.

Flawed points system or not, the numbers are there and the sums add up. The question is about logic and analysis of the information provided, without pre conceptions and without assumptions, whilst not being distracted by trying to decipher information that has been placed within the question to cause doubt but that is actually largely irrelevent to the core question.

When presented with the question, many will assume that the three teams are in a mini league, and that the points they've accumulated are the TOTAL points at the end of the mini tournament. The questions does not state this. It also doesn't state that the percieved mini tournament is incomplete. Your mind is distracted by mis-conceptions and pre-conceptions.

For those reasons, if this question as posed to 100 adults and 100 children, you would probably find that more children worked out the correct answer than adults because children have fewer pre-conceptions.

If that makes any sense at all. Kinda confused myself with the above.

 

[Trazor]

It also doesn't state that the percieved mini tournament is incomplete.

Precisely,so you have to assume it was completed.

The idea was to see the effect of this system on promotion and relegation, hardly possible with an incomplete league.

You may be correct, but I think its a flawed question.

 

[Softus]

You're right, it ain't football - it's maths.

It very much is not maths.

They want kids to try and think outside of the box.

If you're right then it's a poor imitation of an exercise in logic and lateral thought, since it works only by virtue of some tenuous semantics.

Wasn't like that when I as a kid I tell ya!

On the contrary: IIRC, 'twas ever thus.

 

[ninebob]

Unfortunately, the football game was disturbed by the sound of an aircraft trying (and failing) to take off on a conveyor belt in the adjacent field.....