I'm completing exercises from Steve Shreve - Stochastic Calculus for Finance I and I'm stuck on one subtask for which I can't find missing element for 11 stopping times mentioned at the end:

Exercise 4.5. In equation (4.4.5). the maximum is computed over all stopping times in S0. List all t he stopping times in So (there are 26) and from among them, list the stopping times that never exercise when the option is out of the money (there are 11).

But I can find only 10.

Here's intrinsic value tree (for H goes up, for T goes down):

 / \
1   1
 \ /

So out-of-the-money is for HH.

So all stopping times where OTM is not exercised are:

inf inf inf inf
inf inf inf  2 
inf inf  2  inf
inf  2  inf inf
inf  2   2  inf
inf  2  inf  2
inf inf  2   2
inf  2   2   2 
inf  2   1   1
inf inf  1   1

So 10 in summary and I can't find the 11. stopping time. What did I miss?

Thanks for any guidance!



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