The Lowest Score!
In a chess tournament, players get 1 point for a win, 0 points for a loss and
2
1
point for a draw. In a tournament where every player plays against every other player exactly once, the top four scores were 5
2
1
, 4
2
1
, 4 and 2
2
1
. What was the lowest score in the tournament?
This question is from NMTC-AMTI 2011.
Image credit: Dutch National Archives
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4 solutions
1 draw=0.5 points and every player had at least a single draw. So, the least score should be 0.5 , but as answer is an integer so the number would be 1 of!course
0 is also a possibility provided 4th position is tied, the question tells the top four scores... not top four persons... so tie is a possibility... Hence why not 0??
Consider the following case 7th Draws with 6th and wins all 6th Draws with 7th and looses to 5th 5th Draws with 3rd and 4th and wins with "LOOSER", 2nd & 6th 4th Only wins with "LOOSER" and looses to 7th and 6th 3rd Only wins with "LOOSER" and looses to 7th and 6th 2nd Only wins with "LOOSER" and looses to 7th, 6th & 5th "LOOSER" Looses to all
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You must make the same points of the top four players!!
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ya in this way all the top 4 are making the desired points
i agree with u . this should be the case and tie breaker is with the 4th and the 5th position holder.
as 1st player got 5.5 (5w+1d+0L)=(let he win by 3,4,5,6,7)&(draw with 2)
2nd -4.5(4w+1d+1L)=(let he win by 3,5,6,7)&(draw with 1)&(lose with 4 )
3rd -4 (4w+0d+2L) =(let he win by 4,5,6&7)&(lose with 1,2)
4th -2.5(1w+3d+2L)=(let he win by 2)&(draw with 5,6,7)&(lose with 1,3 )
5th -2.5(2w+1d+3L) =(let he win by 6,7)&(draw with 4)&(lose with 1,2,3 )
6th-1 (1w+1d+4L)= (let he win by 7)&(draw with 4)(lose with 1,2,3,5, )
and 7th-0.5(0w+1d+5L) = (lose with 1,2,3,5,6 )&(draw with 4)
but 7 must draw with one which is 4 ....so his score becomes 0.5 and answer becomes 1.
i hope thw whole scenario got cleared.
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Consider the following solution:
1st player got 5.5 (5w+1d+0L)=(let he win by 3,4,5,6,7)&(draw with 2)
2nd -4.5(4w+1d+1L)=(let him win by 4,5,6,7)&(draw with 1)&(lose with 3 )
3rd -4 (3w+2d+1L) =(let him win by 2,6&7)&(lose with 1)& draws with 4,5
4th -2.5(1w+3d+2L)=(let him win by 7)&(draw with 3,5,6)&(lose with 1,2 )
5th -2.5(1w+3d+2L) =(let him win by 7)&(draw with 3,4,6)&(lose with 1,2)
6th-2 (1w+2d+3L)= (let him win by 7)&(draw with 4,5)&(lose with 1,2,3)
and 7th-0(0w+0d+6L) = (lose with 1,2,3,4,5,6 )
Hence 7th gets "0" points...
There is no such condition that everyone must have a draw!!
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@Situ Das – Agree with you.
@Situ Das – ya i agree with u but my case is also right.
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@Nishant Sharma – Yes yours is correct, but we have to find the minimum score right?
100000th ???
no dude even looser loosses to all but to satisfy the conditions and a tie breaker also helds he must draw ..
at least there is one tie as the top score is 5.5....
minimal player requirement 7
1 player has 6 matches with other 6
so the best winner, wins 5 , so 5
1 = 5 and one draw of 1
.5
hence his total score is 5.5
So, for this problem, none can loose all the matches. He has to draw one match at least.
If you are still not satisfied, please try calculating the scores of every player in the match.
Where is written that- every player make at least 1 draw?
yeah..the same way i solve the problem..
yeah...i do that too
I'm unable to infer requirement of 7 players and that "every player had at least a single draw."
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The top player has 5.5 points, so he/she must have played at least 6 matchs. Therefore there must be 7 players or more in the competition.
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Thanks. I can now see 7 players playing the matches.
1 draw=0.5 points and every player had at least a single draw. So, the least score should be 0.5 , but as answer is an integer so the number would be 1 of!course #Suraj
I m nt understanding till nowwwwww
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1 draw=0.5 points and every player had at least a single draw. So, the least score should be 0.5 , but as answer is an integer so the number would be 1 of ! course.
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where is it written that every person had at least one draw??
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@Jay Mandliya – i agree with u bro..why not 1 can loose all matches
Logical
explain in simple manner
hmm
I thought they were just four players...haha,I'm practicing....
I felt complicacy in the question , please help me out..
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1 draw=0.5 points and every player had at least a single draw. So, the least score should be 0.5 , but as answer is an integer so the number would be 1
good
how did u get 7 players
here total points 21 and 4 players covers 16.5 points. but the lowest points of the top 4 players is 2.5...........that says that the highest point of the lower 3 players can't exceed 2(if one has 0 point,then other two have either 2 or 2.5 and it is not possible). so the lowest point of course 1.
Is this regardless of whether the player wins or loses???
solve this The function f(x) satisfies the equation f(x) = f(x−1)+f(x+1) for all values of x. If f(1) =1 and f(2) = 3, what is the value of f(2013)?
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Why do people posts questions on solution comments?
4026
This is a recursive definition of the function f(x) in terms of f(x-1) and f(x+1) which will never hit the base case for the term f(x+1). This equation is unsolvable unless we consider this being computed on a computer which has limitations on the number of bits being used for number representation, which will eventually cause the f(x+1) to overflow and hit the base case only if you have a humongous stack :)
Ans will come to be 2
ans-2
f(2013)=f(2013-1)+f(2013+1)=2012+2014=4026
First of all, the no. of players should be assigned according to the highest score given.Say there are 7 players then give the 7th player highest score accordingly the other players will find there score i.e., since 7th player gets 5.5 score it means he had won 5 matches and drawn 1 match. So give the 0.5 marks of draw to the 6th player and 0 to all other player who played there first match with the 7th player. Then assign 4.5 point to the 6th player by making the play of 5 matches with the remaining 5 players and keep going on in this order. Finally for lowest score we have to make the assumption in the end that the 1st player will only be able to draw the matches. That is what is desired 1st player will be able to earn 0.5+0.5 points.
no i can't get it
not understanding
Did not get it :(
In this order, (omitting loses)
7th player- 5.5 points- 5W, 1D
6th player- 4.5 points- 4W, 1D (In 5 match, with the players below)
5th player- 4 points - 4W, 0D (In 4 match...)
4th player- 2.5 points- 2W, 1D (3 match...)
3rd player- 0.5+...points- ? (2 match...)
2nd player- ? - ? (1 match...)
1st player- ? - ? (0 match...)
How will we continue after giving the 0.5 point to the 3rd player?
here total points 21 and 4 players covers 16.5 points. but the lowest points of the top 4 players is 2.5...........that says that the highest point of the lower 3 players can't exceed 2(if one has 0 point,then other two have either 2 or 2.5 and it is not possible). so the lowest point of course 1.
The scores of the players are as follows: 5-0-1 4-1-1 4-2-0 2-3-1 2-4-0 1-4-1 1-5-0 Only in this condition the number of wins is equal to the number of losses. Hence the lowest score is 1
1 match = 1 point. Again the sum of the points of top 4 players are 16.5. So I counted how many players are at least needed to held 16.5 or much point. And we need at least 7 players in the tournament (Total match will be 6+5+4+3+2+1=21 match). Because the top 4 gained 16.5 points; the other three will have a total of (21 -16.5) or 4.5 point. Because every player make at least one draw and the lowest player has a point of integer number the point of the lowest player should be 1 simply.