A Simple Number Game...

Or is it?
Objective: get to 16
You pick one of the three numbers I say, and I'll give you three more based on that. Get to 16, you win! (Idk if this should be single player or multi player but we'll see how it goes.)
Start (1):
5
10
7
[Finished]-only for reference now

 

& before never gives the number.
Is there a pattern, or are you picking randomly?
7

 

I have a predetermined setup, and the same number will always give the same set. Otherwise no pattern. It's closer to a guessing game but you'll start to make more educated guesses as it goes. A
(If you must know, I have a mini book I made that is this puzzle thingy irl.)
5
9
6

 

Notes:
1) 5, 10, 7
7) 5, 9, 6
-----
5?

 

1
6
7
Also note: changed 15 to 16 goal, forgot that 15 leads to 16 which is win

 

1) 5, 10, 7
7) 5, 9, 6
5) 1, 6, 7
Guess: 6

 

5
3
1
Sorry, disregard my earlier comment about page 15 leading to 16, that was wrong I didn't know the book as well as I thought

 

1) 5, 10, 7
7) 5, 9, 6
5) 1, 6, 7
6) 5, 3, 1
Guess: 3

 

12
6
13

 

1) 5, 10, 7
3) 12, 6, 13
5) 1, 6, 7
6) 5, 3, 1
7) 5, 9, 6
Guess: 12

________________________________

 

1) 5, 10, 7
7) 5, 9, 6
5) 1, 6, 7
6) 5, 3, 1
3) 12, 6, 13
Guess: 12

 

4
15
5
(Remember 15 doesn't directly lead to 16 like I misspoke earlier)

 

The OP says get to 15 still but the objective says get to 16. I’m assuming it’s get to 16?

 

Right, sorry forgot I mentioned 15 twice

 

Okay.

1) 5, 10, 7
7) 5, 9, 6
5) 1, 6, 7
6) 5, 3, 1
3) 12, 6, 13
12) 4, 15, 5
Guess: 4

 

10
2
3

 

1) 5, 10, 7
7) 5, 9, 6
5) 1, 6, 7
6) 5, 3, 1
3) 12, 6, 13
12) 4, 15, 5
4) 10, 2, 3
Guess: 2

 

4
8
10

 

1) 5, 10, 7
7) 5, 9, 6
5) 1, 6, 7
6) 5, 3, 1
3) 12, 6, 13
12) 4, 15, 5
4) 10, 2, 3
2) 4, 8, 10
Guess: 8

 

2
13
9