In a best-of-five tennis match Pete Shamprowess led André Allgassy the whole way during the first two sets. André won more games in the first set than in the second. Pete won the first game in the third set. Pete won the match, even though André won 25% more games.
What were the scores in each of the 5 sets?
clc
scoresS=[7,6;7,5;6,4;6,3;6,2;6,1;6,0];
scoresA=flip(scoresS,2);
for g1=1:size(scoresS,1)
for g2=1:size(scoresS,1)
for g3=1:size(scoresA,1)
for g4=1:size(scoresA,1)
for g5=1:size(scoresS,1)
scoreSet=[scoresS(g1,:);
scoresS(g2,:);
scoresA(g3,:);
scoresA(g4,:);
scoresS(g5,:);
];
pete=scoreSet(:,1);
andre=scoreSet(:,2);
if 5*sum(pete)==4*sum(andre) ...
&& andre(1)>andre(2) ...
&& pete(3)>0
disp(scoreSet)
disp(' ')
end
end
end
end
end
end
finds these four sets of statistics for the match:
PS AA
7 6
6 4
1 6
0 6
6 3
7 6
6 3
1 6
0 6
6 4
7 5
6 4
1 6
0 6
6 4
6 4
6 3
1 6
0 6
7 6
The first three match scores all involve a tie breaker in the first set, or at least having gone through a score of 5-5, contradicting the statement that Pete led all the way through the first two sets. The final grouping above is the requested scoring:
Pete Andre
6 4
6 3
1 6
0 6
7 6
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20 25
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Posted by Charlie
on 2024-03-25 10:27:04 |
computer-aided solution
