Problem 213

[Tommy137]

4 1 4.778

This is correct.

4 2 5.338
4 3 5.639

These two are not

[LarryC]

Thanks for the reply!

Would you mind giving me those case values? I have more values I wish to check...

[Tommy137]

Thanks for the reply!

Would you mind giving me those case values? I have more values I wish to check...

PM'ed you.

[LarryC]

Thanks Tommy! As it happens, though, I've already completed it.

I think that is probably the second hardest Project Euler (for me). The hardest not being 198, however!

[Tommy137]

Thanks Tommy! As it happens, though, I've already completed it.

I saw it a few minutes after I send you the values

I think that is probably the second hardest Project Euler (for me). The hardest not being 198, however!

I agree with 198 not being the hardest... I still have no idea how to even approach Problem 208 (View Problem)

[quilan]

Unrelated, but am I one of the only ones that thought 198 really wasn't all that difficult? Especially considering we've had another earlier problem that practically gave away one method of solving it?

[hk]

Yes but many did not solve that earlier problem in one of the intended ways. That's no problem if one studies afterwards how it should have been solved to be prepared for a follow up. Obviously they failed to do so.

[LarryC]

Yay! I'm a 100%-er again after a long gap!

Anyway, 198 definitely was a tough one but this one I just failed to wrap my brain around so to speak. Most of the other probability questions have been fine but this one was extremely tough for me!

[Ikcelaks]

Most of the other probability questions have been fine but this one was extremely tough for me!

I loved this problem in part because, while it didn't require any sort of advanced knowledge, it really tested your understanding of the fundamentals of probabilites and expected values.

Unrelated, but am I one of the only ones that thought 198 really wasn't all that difficult? Especially considering we've had another earlier problem that practically gave away one method of solving it?

For that very reason, 198 was essentially trivial for me. Meanwhile, 202, which many have solved, was extraordinarily elusive. Clearly, there is no such thing as a toughest problem on any remotely absolute scale.

[quilan]

I don't know... 177 & 184 seem to me the hardest problems that have been on this site bar none.

[axelbrz]

Hi, are these expected values correct for a 4x4 matrix?:

Bell 1: 4.777778
Bell 2: 1.941406
Bell 3: 3.505002
Bell 4: 2.589931
Bell 5: 3.114868

Thanks!

[Tommy137]

Hi, are these expected values correct for a 4x4 matrix?:

Bell 1: 4.777778
Bell 2: 1.941406
Bell 3: 3.505002
Bell 4: 2.589931
Bell 5: 3.114868

Thanks!

Only the first value is correct.

[viv_ban]

As pointed earlier, the expected number of empty square after one toll is equal to 1 in case of 2X2 grid. Will it remain the same forever(i.e. remains 1 irrespective of number of tolls).

[daniel.is.fischer]

Yes.

[viv_ban]

I am sure that my algorithm is correct but I am still not getting the right answer.
Can anybody please tell me if I am correct for the following values:
expected empty cells for 4X4 after 2 tolls are 4.86548889746 and after 50 tolls are 4.93827160494
in case of 20X20 after 50 tolls expected empty cells are 126.37819102.

thanks.

[daniel.is.fischer]

No, all those are wrong.

[Assato]

Wow, I must be doing something seriously wrong then... my simulations give:

<deleted - ed_r>

[ed_r]

I've deleted your simulation results, which are potential spoilers. Seems your simulation works just fine.

[Assato]

Oh, sorry, I posted because I was about sure they were wrong... I read in the last page it was close to 147, but didn't realize that was a 20x20 simulation!

[quilan]

Oh, sorry, I posted because I was about sure they were wrong... I read in the last page it was close to 147, but didn't realize that was a 20x20 simulation!

Yeah, I was being particularly tricky...