Justification:

Cheng is 25 points behind Ben.

Aisha is 22 points behind Ben.

Together, they are 47 points behind Ben.

Together they can win at most 10 (8+2) points and ben will win at least 1 point.

At each game they can win 9 points more than Ben.

They are 47 points behind wich mean they need to play at least 6 games to catch up with him (round up 47/9)

**The number of additional games is at least 6.**

After each game 11 points are added to the total of their scores.

If the players have the same score, the total of their scores is a multiple of 3.

Let n be the number of additional games

12+9+34+11n is a multiple of 3

iff 12+9+33+1+11n is a multiple of 3

iff 1+11n is a multiple of 3.

iff n=1+3k for any `k in NN`

**Therefore, the number of games will be 1, or 4, or 7, or 10....**

In conclusion, The number of additional games is at least 6, in the form of 1+3k

We have a solution with 7 games

**Therefore the munimum number of additional games is 7.**

A solution in **7 additional weeks:**

Aisha 8 8 8 2 2 2 2

Ben 2 2 2 1 1 1 1

Cheng1 1 1 8 8 8 8

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