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No problem, see you later.
Party music? Serves him right.
Long time ago, it's correct.
Also, I checked, the above matrix is working.
Some do have meaning. Most are some silly party songs, though.
You're welcome. It wasn't that hard, though.
I think I might be able to reduce it to 5 states.
Edit: This should work too:
Sorry, forgot.
In order: *A*BC, A*B*C, AB*C*, *A*B, A*B*, *A*C, A*C*, A, B+C.
You are becoming more musical by the day.
It can, I have the matrix. It's quite big, though.
What song?
It is not, but that is my solution.
Ah, sorry.
Well, it's very stupid.
I already did.
I can post it, but the fact that it's close is just a coincidence here. It would get that number whatever the probabilities were.
Hm, your simulation is incorrect. You are not calculating the probability correctly.
Good pixels go to heaven. Bad pixels go on to make up the BSoD.
It works for any number of digits, also.
Yes, sorry. I was just checking to see if I have messed up.
I need to get into form a bit, haven't done much math in the last 3 months.
I have solved it, and I'm pretty sure of the answer. The simulation and the analytic method agree.
Not sure if this is correct, but I am getting:
91 does seem more appropriate.
What happenes when the lines do not cross and are not parallel? We are in R3.
To have only 9 states, you can merge the cases where only B is left, only C is left, B and C are left with B being asked first, B and C are left with C being asked first and use that one as an absorbing state.
I'll post the sim as soon as possible.
EDIT: Here it is:
Count[Table[Block[{l = {1, 2, 3}},
While[Length[l] > 1,
r = RandomReal[];
If[(Length[l] > 1) && (r < 1/5), l = DeleteCases[l, 1]];
r = RandomReal[];
If[(Length[l] > 1) && (r < 1/2), l = DeleteCases[l, 2]];
r = RandomReal[];
If[(Length[l] > 1) && (r < 9/10), l = DeleteCases[l, 3]];];
l
], {1000000}] // Flatten, 1]/1000000 // NHm, got the sim working and it got the same answer. The probability of no. 1 staying last is 121/184, so the probability we want is 63/184.
Ah, okay.
Did you ever try listening to newer music?