# Why is this tsumego solution wrong?

I'm trying to understand why my solution to this tsumego is incorrect. It's "Basic problem #26" from Tsumego Pro and looks like this:

``````\$\$ ----------------------------
\$\$ . . . . . . . . X . O X . . |
\$\$ . . . . . . . . X O . O O O |
\$\$ . . . . . . . X . X O O X . |
\$\$ . . . . , . . . . X X X X . |
\$\$ . . . . . . . . . . . . . . |
\$\$ . . . . . . . . . . . . . . |
\$\$ . . . . . . . . . . . . . . |
``````

The built-in correct solution is this:

``````\$\$ ----------------
\$\$ . . X 3 O # 1 2 |
\$\$ . . X O . O O O |
\$\$ . X . X O O X . |
\$\$ . . . X X X X . |
``````

(alternatively, after (2), with black playing at the marked position again and white taking once more by playing at (1), and only then black playing at (3)). I understand why this solution is correct, just not why mine isn't.

The following is my solution, which the program marks as incorrect.

``````\$\$ ----------------
\$\$ . . X 1 O X 2 . |
\$\$ . . X O . O O O |
\$\$ . X . X O O X . |
\$\$ . . . X X X X . |
\$\$ . . . . . . . . |
``````

(white's response at (2) is built into the program, the rest of the white moves aren't).

``````\$\$ ----------------
\$\$ . . X X O . O . |
\$\$ . . X O a O O O |
\$\$ . X . X O O X b |
\$\$ . . . X X X X . |
\$\$ . . . . . . . . |
``````

If black now takes the ko at (a), the only thing white can do (that I can see) is play at (b) in order to try escaping on the right side. It can't play anywhere on its inside because that would essentially be suicide, and because for black winning the ko means connecting its two groups, I don't see any possible white threat that black would have to respond to.

``````\$\$ ----------------
\$\$ . . X X O . O . |
\$\$ . . X O 3 O O O |
\$\$ . X . X O O X 4 |
\$\$ . . . X X X X . |
\$\$ . . . . . . . . |
``````
``````\$\$ ----------------
\$\$ . . X X O . O . |
\$\$ . . X 5 X O O O |
\$\$ . X . X O O X O |
\$\$ . . . X X X X 6 |
\$\$ . . . . . . 7 8 |
\$\$ . . . . . . 9 0 |
``````

This could now continue all the way to the bottom of the board (not shown), at which point the white group has no liberties left except for the eye-and-a-half at the top. If white decides to stop running away, I still don't see anything forcing it could play to stop black from closing (e.g. at (10)).

In the end black can take:

``````\$\$m37
\$\$ ----------------
\$\$ . . X X O 1 O 3 |
\$\$ . . X X X O O O |
\$\$ . X . X O O X O |
\$\$ . . . X X X X O |
\$\$ . . . . . . X O |
\$\$ . . . . . . X O |
``````

with no useful response (38) for white.

What is it that I'm missing? Where could white have lived?