Record 24b9a22163934adba59a3188c7528a8f

Here is a short Python program.

```python
spare = 9
scores = [4, 1, 6]
shift = 1
scores = scores + [spare]
limit = shift + 3
limit = limit // 2
limit = limit * 2 - 8
score = spare
limit += shift
limit += 6
limit = limit * 2 - 7
if spare >= shift:
    spare += shift * 2
limit = limit * 2 - 6
limit += 2
limit -= 9
limit -= 8
limit += 6
spare += len(scores)
limit += shift
limit += 1
limit += 8
scores[-1] = 0
limit += 2
limit -= 2
scores = scores + [spare]
spare += limit
```

After this program runs, what is the value of `spare`? Work through it carefully, then give the final answer on its own last line as `ANSWER: <python literal>`.

To find the final value of `spare`, let's trace the program step-by-step:

1.  `spare = 9`
2.  `scores = [4, 1, 6]`
3.  `shift = 1`
4.  `scores = scores + [spare]` $\rightarrow$ `scores = [4, 1, 6, 9]`
5.  `limit = shift + 3` $\rightarrow$ `1 + 3 = 4`
6.  `limit = limit // 2` $\rightarrow$ `4 // 2 = 2`
7.  `limit = limit * 2 - 8` $\rightarrow$ `2 * 2 - 8 = 4 - 8 = -4`
8.  `score = spare` $\rightarrow$ `score = 9`
9.  `limit += shift` $\rightarrow$ `-4 + 1 = -3`
10. `limit += 6` $\rightarrow$ `-3 + 6 = 3`
11. `limit = limit * 2 - 7` $\rightarrow$ `3 * 2 - 7 = 6 - 7 = -1`
12. `if spare >= shift:` $\rightarrow$ `9 >= 1` is **True**.
    *   `spare += shift * 2` $\rightarrow$ `9 + (1 * 2) = 11`
13. `limit = limit * 2 - 6` $\rightarrow$ `-1 * 2 - 6 = -2 - 6 = -8`
14. `limit += 2` $\rightarrow$ `-8 + 2 = -6`
15. `limit -= 9` $\rightarrow$ `-6 - 9 = -15`
16. `limit -= 8` $\rightarrow$ `-15 - 8 = -23`
17. `limit += 6` $\rightarrow$ `-23 + 6 = -17`
18. `spare += len(scores)` $\rightarrow$ `len([4, 1, 6, 9])` is 4. `11 + 4 = 15`
19. `limit += shift` $\rightarrow$ `-17 + 1 = -16`
20. `limit += 1` $\rightarrow$ `-16 + 1 = -15`
21. `limit += 8` $\rightarrow$ `-15 + 8 = -7`
22. `scores[-1] = 0` $\rightarrow$ `scores = [4, 1, 6, 0]`
23. `limit += 2` $\rightarrow$ `-7 + 2 = -5`
24. `limit -= 2` $\rightarrow$ `-5 - 2 = -7`
25. `scores = scores + [spare]` $\rightarrow$ `scores = [4, 1, 6, 0, 15]`
26. `spare += limit` $\rightarrow$ `15 + (-7) = 8`

Final value of `spare` is 8.

ANSWER: 8

(no reasoning captured)