# What is the smallest number of additional weeks that will allow them to have the same score?Aisha, Ben and Cheng entered a weekly school competition. In each week they participated, the three of...

What is the smallest number of additional weeks that will allow them to have the same score?

Aisha, Ben and Cheng entered a weekly school competition. In each week they participated, the three of them came first, second and third in some order. The score for 1st place was 8, for 2nd place it was 2 and for 3rd place it was 1. At one stage, the total score for Aisha was 12, for Ben it was 34 and for Cheng 9.

After a few weeks, Aisha, Ben and Cheng had the same score. What is the smallest number of additional weeks that will allow them to have the same score?

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### 2 Answers

Aisha, Ben and Cheng entered a weekly school competition. In each week they participated, the three of them came first, second and third in some order. The score for 1st place was 8, for 2nd place it was 2 and for 3rd place it was 1. At one stage, the total score for Aisha was 12, for Ben it was 34 and for Cheng 9.

After a few weeks they have the same score. Let the minimum number of weeks for this to happen be n. After n weeks if they haveĀ the same score N, Ben should earn N - 34 points, Aisha N - 12 and Cheng N - 9

If Cheng comes 1st for 4 weeks with Aisha coming 2nd and Ben coming 3rd, their scores are Aisha: 20, Ben: 38 and Cheng 41. Now if Aisha comes 1st for the next 3 weeks, Ben 2nd and Cheng 3rd their scores areĀ equal at 44.

**It would take a minimum of 7 weeks for their scores to become equal.**

### User Comments

Thankyou for all your help but I didn't actually need it in the end as I worked it out. Thankyou ^ though. Please, don't feel like anyone else needs to answer coz I don't want them too!