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. how many weeks did they take to achieve these scores?

Question

amistre64 · Answer

5 * 11 = 55 yes; but we cant have a score of 5 each week; so it would have to at least be a score of 11 each week for 5 weeks, but thats not taking into account who wins what spot

amistre64 · Answer

1 2 8
1 3 7   2 3 6
1 4 6   2 4 5

are all the possible 11 scores I can think of

anonymous · Answer

Nice , I didn't entirely think that through . Amistre does it again. Nice man.

amistre64 · Answer

the other issue would be if we can construct a suitable set of places to match the totals given with these, if not we would have to reconfigure it

amistre64 · Answer

A: 8 1 1 1 1 = 12
B: 2 8 8 8 8 = 34
C: 1 2 2 2 2 =   9
------------------
      5 weeks = 55