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12. Swimming Teams

Teams from two schools compete in a swimming match. Each team has two members for each event. The scoring is 5 points for first place, 3 for second, 2 for 3rd and 1 for 4th place. After six events no one has been disqualified and the score of the school in the lead is the reverse of the other school's score. What is the difference between their two scores?
 

Scroll down the page for the answer.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

points available for each event = 5 + 3 + 2 + 1 = 11

points available for 6 events = 66

if one score is the reverse of the other then possible scores are:
 
1.   15 and 51
2.   24 and 42
3.   33 and 33

3 is not allowed since there would be 'no school in the lead'

after six events, even if a team came 3rd and 4th every time, the minimum score is 18 so 1 is not an option either

so 2 is the only option and the difference between their scores is 18
 

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