Computing Games

When I was twelve I had a mathematics teacher who started his lessons with his so-called computing game.

At the beginning of the lesson he wrote a sequence of arithmetic operations on the board, say +7, *3, -15, /3. Then everybody had to get ready and he started the game by saying the start number, say 20. Our task was to perform the four operations in our head and then start with the first operation again.
In the example above you would get the sequence 27, 81, 66, 22, 29, 87, 72, 24, ... and so on.

After 30 seconds he shouted "STOP!". Then you had to write down the number you currently had. Finally he checked our solutions with his list. If your number didn't appear on his list, you had made an error and received a score of zero. Otherwise you received one point per operation. In the example above, 24 would have been a score of 8 points.

Am I silly? What a stupid exercise. Of course I started the computation right after he had written down the operations: x+7, 3x+21, 3x+6, x+2, ... there we are: each cycle simply is a +2 operation.
I waited for the start number, he said 20, I wrote down 42, leaned back and relaxed. 44 points should be enough.

When he checked the solutions 42 didn't appear on his list. He didn't expect anybody to reach more than 20 points so his list was too short. Zero points.

I got angry. I wanted my 44 points. After all, I made 11 complete cycles!
The problem was that we hadn't learned algebra in school yet. So I thought that doing computations with variables was an ingenious trick invented by me and I wanted to keep it a secret.

Thus I didn't tell him how I got the result. I received a score of zero and the teacher probably thought I was lazy and bad in mathematics.