Team India Special

Probability Level 5

In the name of our player of the tournament.

After this year's performance M.S.Dhoni and team India sat together to plan for the next tournament.

This is a different type of tournament.

In the next tournament 100 teams are going to participate. Each team will play a single match with all other teams.Team would be awarded a score of 4 upon winning a match, a score of 0 upon losing a match and each of the two will be awarded a score of 2 when it ends in a draw.

What is the minimum score team India has to score to ensure that it is in top 10.

This is part of my set : Fun is a Student's Right

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The answer is 378.

2 solutions

Mayank Singh
Apr 6, 2016

My plan is to find the 10th highest score that a team can achieve.

Lets say a team wins x matches and draws y matches.

See that x+y<=99

Score of the team is 4x+2y=4(x+y/2)

The score DOESNOT depend on individual values of x and y, but a combined value x+y/2

which can take values :

99, 98.5, 98, .....

Find the 10th term of this A.P.

It is 94.5

Score is 4*94.5=378

I have a doubt in your solution

Your series of points comes out to be 396,394,392........100 terms whose sum = 29700..

But if you see ...total matches that can be played in the tournament is 4950 ...so the total score that can be achieved is 19800 which is contradicting to your answer....

Or in other words the series you are talking about is not possible... You only see if the first player got 396 (that is max score) it implies that he has won all the matches So the second player has lost al least one match so his score must be <= 392...

Aniket Sanghi - 5 years, 2 months ago

Yes I totally agree to your point, that the given series CAN'T be achieved SIMULTANEOUSLY

Your question asked how much score India must possess to ENSURE their rank in top 10.

So I've assumed the worst case where India must score the 10th highest score

Mayank Singh - 5 years, 2 months ago

I think that the worst case would be the one mentioned in my solution

Aniket Sanghi - 5 years, 2 months ago

@Aniket Sanghi – Why is that the worst case?

Mayank Singh - 5 years, 2 months ago

@Mayank Singh – I could find only that one ........by symmetry......may be that's the only one ..........yours can't be the case as it is not possible.....In my opinion it isn't valid.......may be I am wrong.....I would be glad if you could correct me

Aniket Sanghi - 5 years, 2 months ago

@Mayank Singh – i think answer is 182

Khushal Sethi - 5 years, 2 months ago

@Aniket Sanghi – assume india score is x. rest 90 teams have score of x-2. total score is 100 * 99 * 2=19800. rest above teams can score a maximum of 99* 4* 9 points. x+90(x-2)+99 * 4 * 9=19800.

x=180.39. not possible . minimum score of india should be 182 .

Khushal Sethi - 5 years, 2 months ago

Aniket Sanghi
Apr 4, 2016

If you will check it out ,

The best possible case is (By symmetry) :

Let a1, a2, a3,.........a100 be the teams.

a1,a2,a3.......a10. , all these 10 teams ends in draw with each other.Rest of the matches(that they play with the other 90 teams) are won by them.

Giving all these an equal score of 378. So the best score that the team in 10th position can score is 378. Hence India has to score a minimum of 378 to be in top 10.

In your santa question : "the end the Santa informed him that he had not distributed a single gift at its correct place".and then you say "boy has given the gift that he was to give in House no. 1, in the House no. 2 in the street." please help me to understand the question

Gauri shankar Mishra - 5 years, 2 months ago

Only one thing is per informed that the gift the he was to give in h no.1 That one he has given in h no.2..........one of the gifts location .you know

Aniket Sanghi - 5 years, 2 months ago

Team India Special

The answer is 378.

2 solutions

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