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. After 5 weeks, the total score for Aisha was 12, for Ben was 34 and for Cheng 9.
What are the number of points earned for 1st, 2nd and 3rd place?

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. After 5 weeks, the total score for Aisha was 12, for Ben was 34 and for Cheng 9. 
What are the number of points earned for 1st, 2nd and 3rd place?

anonymous · Answer

let a=points for first    b=second    c=third
every week a+b+c points were awarded, so
5(a+b+c) = 12+34+9
a+b+c = 11 points each week among the 3
since a,b,c are positive integers, 
there are only a few possibilities for (a,b,c):
(5,4,2) (6,3,2) (6,4,1) (7,3,1) or (8,2,1)
and using trial and error I see that (8,2,1) works
week  A   B   C
   1     8   2   1
   2     1   8   2
   3     1   8   2
   4     1   8   2
   5     1   8   2
------------
        12 34   9

Phi probably gave a more rigorous solution, but I hope this helps
there are lots of ways to look at and solve any problem

anonymous · Answer

thanks

anonymous · Answer

But the three must've been 1st, 2nd or 3rd in some time, it says.