Question

Aisha, Ben and Cheng entered a weekly school competition. In each week, the three of them came first second and third in some order. The scores for the top 3 places are positive integers and the same each week. The score for first place was more than the score for second place which was more than the score for third place. Aisha won in the first week. At one stage the total score for Aisha was 12, for Ben was 34 and for Cheng 9. After some more weeks, they all had the same score. What is the smallest number of weeks which will allow them to have the same score?

Answer 1

long word problem o.O

Answer 2

!!

Answer 3

I can't give you much help... But some tip:

A B C have 6 possible combinations:
A,B,C
1,2,3
1,3,2
2,1,3
2,3,1
3,1,2
3,2,1

And in the first week there were two possible combinations:

1,2,3 or 1,3,2 ~~ Since A won first place~~

This means that in the weeks following, B won all or most 1st places. For A to catch up, it had to be less winning than C... If you think this through you may come up with an answer on how many weeks it takes them to actually catch up... but I don't know how to do that.. However, if you write some of these working, and if points/marks are awarded, some of these workings may give you some points, even if you can't get to the answer.... But keep trying!!