SOLUTION: I am completely stumped on this one: 3 colleges participated in a track and field competition. Each college sent only 1 representative to each event. Jessica a student at Kennedy

Question 118758: I am completely stumped on this one:
3 colleges participated in a track and field competition. Each college sent only 1 representative to each event. Jessica a student at Kennedy college went to the competition to cheer on her boyfriend the long jump champion.
After the competition her roommate asked her how their school performed. Jessica told her they won the long jump but Jefferson College won the competition with 22 points. Kennedy and Adams college only got 9 points.
Kelly asked what the point system was. Jessica didn't know but said they gave a different number of points for each place and awarded points for 1st, 2nd & 3rd and the point system was the same for each event.
Kelly asked how many events there were but Jessica didn't know that either.
Kelly's friend Jack asked if there was a javelin throw. Jessica said there was. Jack asked who won but Jessica didn't know.
Here is the problem question: Who won the javelin throw? I have to clearly and logically show how I got my answer. No guessing and I have to use math and logic to solve it.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
3 teams; one representative to each event; 1st, 2nd and 3rd place points
___ so each team is awarded points from each event

40 total points (22+9+9) ___ different values for each place (1st,2nd,3rd)
___ lowest possible total from each event is 6 (3+2+1), but 6 is NOT a factor of 40
___ point totals from each event must be 8 or 10 ___ 20 is too big
___ so there were either 4 or 5 events

possible point values
5 events ___ 1-2-5, 1-3-4
4 events ___ 1-2-7, 1-3-6, 1-4-5, 2-3-5

Kennedy took at least 1 first place, but tied with Adams for the lowest score with 9
___ this eliminates ALL the 4 event possibilities

Jefferson won with 22 ___ this eliminates 1-3-4 (4*5=20)
___ they won the javelin (and everything else, except the long jump)

J __ 5-5-5-5-2
K __ 5-1-1-1-1
A __ 2-2-2-2-1
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