Here are the results of a contest with 9 players: Team 1 was better than team(s)
ID: 3195273 • Letter: H
Question
Here are the results of a contest with 9 players:
Team 1 was better than team(s): 8, 9
Team 2 was better than team(s): 1, 5, 6
Team 3 was better than team(s): 1, 2, 4, 5, 6
Team 4 was better than team(s): 1, 2, 6, 7, 8
Team 5 was better than team(s): 1, 4, 7
Team 6 was better than team(s): 1, 5
Team 7 was better than team(s): 1, 2, 3, 6
Team 8 was better than team(s): 2, 3, 5, 6, 7
Team 9 was better than team(s): 2, 3, 4, 5, 6, 7, 8
Find a ranking of the 9 teams such that each team is better than the one ranked immediately after it (the first team is better than the second, the second is better thatn the third, etc.) such that team 1 is ranked in position 7. There may be more than one correct answer.
Explanation / Answer
1) 1>8,9
2) 2> 1,5,6
3) 3>1, 2, 4, 5, 6
4) 4>1, 2, 6, 7, 8
5) 5>1, 4, 7
6) 6>1,5
7) 7>1, 2, 3, 6
8) 8 >2, 3, 5, 6, 7
9) 9>2, 3, 5, 6, 7,8
if we look closely we get: 9>8 , 8>7 , 7>6 , 6>5 , 5>4
combining all these we get : 9>8>7>6>5>4.........(a)
from 1 and a we get : 1>9>8>7>6>5>4..................(b)
from 2 and b we get : 2>1>9>8>7>6>5>4.............(c)
from 3 and c we get : 3>2>1>9>8>7>6>5>4 this is the first arrangement.
from 1 and 6 we get : 6>1>8.............(d)
from 8 and d we get : 6>1>8>3............(e)
from 3 and e we get : 6>1>8>3>4..........(f)
from 9 and f we get : 9>6>1>8>3>4............(g)
from 4 and g we get : 9>6>1>8>3>4>2..........(h)
from 2 and h we get : 9>6>1>8>3>4>2>5..........(i)
from 7 and i we get : 9>6>1>8>3>4>2>5>7 this is the second arrangement.
from 1 and 7 we get : 7>1>9..........(j)
from 9 and j we get : 7>1>9>2.............(k)
from 2 and k we get : 7>1>9>2>6...........(l)
from 6 and l we get : 7>1>9>2>6>5.........(m)
from 5 and m we get : 7>1>9>2>6>5>4.......(n)
from 4 and n we get: 7>1>9>2>6>5>4>8.....(o)
from 8 and o we get : 7>1>9>2>6>5>4>8>3 this is the third arrangement.
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