Thanks! You just caught a typo in my book - unfortunately after it was published. It's amazing how a finite-sized book can have an infinite number of typos.

Speaking of mistakes: in my lecture above I originally wrote:

> Your goal is to start at state 10 and move all the way to state 50. Since you're bossing lots of people around, you can make them do tasks simultaneously. However, you can only reach a state after you have reached _all_ its predecessors! For example, you can't reach state 50 unless you have already reached states 20, 30 _and_ 40.

This was wrong; this is not how people usually use PERT charts. The usual rules say that you can only reach a state after you have accomplished all the tasks leading up to that state - i.e., traversed all the edges pointing into that state.

Based on my erroneous statement of the rules, [Sophie Libkind got a different answer to Puzzles 56 and 57](https://forum.azimuthproject.org/discussion/comment/17832/#Comment_17832) - different than the answer by Jared Summers based on the _usual_ rules.

This led to an interesting discussion which will only make sense if you know my original mistake! I'm going to correct my lecture now, but please compare what I had written:

> Your goal is to start at state 10 and move all the way to state 50. Since you're bossing lots of people around, you can make them do tasks simultaneously. However, you can only reach a state after you have reached _all_ its predecessors! For example, you can't reach state 50 unless you have already reached states 20, 30 _and_ 40.

to what's there now:

> Your goal is to start at state 10 and move all the way to state 50. Since you're bossing lots of people around, you can make them do tasks simultaneously. However, you can only reach a state after you have done _all_ the tasks leading up to that state. For example, you can't reach state 50 unless you have already done _all_ of tasks C, E, and F.

The change makes a big difference.

Speaking of mistakes: in my lecture above I originally wrote:

> Your goal is to start at state 10 and move all the way to state 50. Since you're bossing lots of people around, you can make them do tasks simultaneously. However, you can only reach a state after you have reached _all_ its predecessors! For example, you can't reach state 50 unless you have already reached states 20, 30 _and_ 40.

This was wrong; this is not how people usually use PERT charts. The usual rules say that you can only reach a state after you have accomplished all the tasks leading up to that state - i.e., traversed all the edges pointing into that state.

Based on my erroneous statement of the rules, [Sophie Libkind got a different answer to Puzzles 56 and 57](https://forum.azimuthproject.org/discussion/comment/17832/#Comment_17832) - different than the answer by Jared Summers based on the _usual_ rules.

This led to an interesting discussion which will only make sense if you know my original mistake! I'm going to correct my lecture now, but please compare what I had written:

> Your goal is to start at state 10 and move all the way to state 50. Since you're bossing lots of people around, you can make them do tasks simultaneously. However, you can only reach a state after you have reached _all_ its predecessors! For example, you can't reach state 50 unless you have already reached states 20, 30 _and_ 40.

to what's there now:

> Your goal is to start at state 10 and move all the way to state 50. Since you're bossing lots of people around, you can make them do tasks simultaneously. However, you can only reach a state after you have done _all_ the tasks leading up to that state. For example, you can't reach state 50 unless you have already done _all_ of tasks C, E, and F.

The change makes a big difference.