[Andrew_S]

But the way you defined the problem (starting already in the top left cell) the number of down steps is 4 and the number of steps right is 10.

So we calculated (14 !) / ((10 !) x (4 !)) = 1 001

which is correct.

Anyway, take your grid problem and let's extend it somewhat.

Imagine that going to the right the grid continues to infinity. We start in the top left cell (column 1, row 5), as in your problem, and at each step go down or right with equal probability. On reaching the bottom row the path stops and that path has a length equal to the number of right steps plus one (so the same as the column number).

The question is this: what's the probability distribution for the path length (column where it reaches the bottom row).

I don't have an equation for the probability mass function but I could calculate it to a high degree of precision.

How would you do it?

[jasonraymondson]

Isn't that just the same kind of problem that was posted here earlier in the flash game?

[Opies]

Why is everyone sitting around doing high school math problems?

Math isn't that fun...
Maybe it's just me

[Andrew_S]

$this->bbcode_second_pass_quote('jasonraymondson', 'I')sn't that just the same kind of problem that was posted here earlier in the flash game?

[Bas]

$this->bbcode_second_pass_quote('jasonraymondson', 'A')ctually 14! is far more.

No problem. I am having alot of fun with these. I try to work them out and when I can I'll post them on here.

[Andrew_S]

$this->bbcode_second_pass_quote('jasonraymondson', 'H')ere is a slightly easier problem

If you have 22 Teams, what are all of the possible combinations of those teams finishing 1st throught 8th Place

[Bas]

the first one was also textbook stuff, but if you haven't seen the textbook for more than ten years it does require some excersize to get in shape again.

[Bas]

$this->bbcode_second_pass_quote('Opies', 'W')hy is everyone sitting around doing high school math problems?

Math isn't that fun...
Maybe it's just me

[jasonraymondson]

$this->bbcode_second_pass_quote('Andrew_S', '')$this->bbcode_second_pass_quote('jasonraymondson', 'H')ere is a slightly easier problem

If you have 22 Teams, what are all of the possible combinations of those teams finishing 1st throught 8th Place

[jasonraymondson]

$this->bbcode_second_pass_quote('Opies', 'W')hy is everyone sitting around doing high school math problems?

Math isn't that fun...
Maybe it's just me

[Andrew_S]

The problem I described about the probability mass function of the path length isn't entirely trivial: it is a much simplified version of a technique I use to calculate evolutionary distances between microsatellite alleles (these are repeated DNA units which mutate quickly and are used for DNA fingerprinting and to study population relationships among other things).

In the real problem the step-size (how men cells you go at the next step) can vary probabilistically and you can move farther away from the target row as well as towards it. Also you can have many pairs of different allele loci mutating simulataneously which makes the probability distributions highly complex.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('jasonraymondson', ' ')Our resident math instructor didn't even attempt the problem

[jasonraymondson]

$this->bbcode_second_pass_quote('PenultimateManStanding', '')$this->bbcode_second_pass_quote('jasonraymondson', ' ')Our resident math instructor didn't even attempt the problem

[jasonraymondson]

$this->bbcode_second_pass_quote('Andrew_S', 'T')he problem I described about the probability mass function of the path length isn't entirely trivial: it is a much simplified version of a technique I use to calculate evolutionary distances between microsatellite alleles (these are repeated DNA units which mutate quickly and are used for DNA fingerprinting and to study population relationships among other things).

In the real problem the step-size (how men cells you go at the next step) can vary probabilistically and you can move farther away from the target row as well as towards it. Also you can have many pairs of different allele loci mutating simulataneously which makes the probability distributions highly complex.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('jasonraymondson', '
')I wish I had known you had a degree in Geology, I would have had a ton of questions for you last semster. I hated that class.

[jasonraymondson]

$this->bbcode_second_pass_quote('PenultimateManStanding', '')$this->bbcode_second_pass_quote('jasonraymondson', '
')I wish I had known you had a degree in Geology, I would have had a ton of questions for you last semster. I hated that class.

[PenultimateManStanding]

Yes, but you didn't say what your field of interest is. I studied Geology because I wanted to know about it. This whole career thing is doomed anyway. Radiology takes energy.

[Carlhole]

Well, I didn't get Jayson's paths problem but here's one I DID get years ago:

A son of a mathematician needs money for books and college tuition. So he writes a note to his father which says:

[align=center][/align]

His father gets the note, thinks for a bit, and then writes a check for the total of books and tuition. What were the amounts?

I haven't re-solved it to get the answer again. But I know HOW I solved it. And the correct answer will be self-evident to anyone who does get it because the sum will make sense.

[jasonraymondson]

$this->bbcode_second_pass_quote('PenultimateManStanding', 'Y')es, but you didn't say what your field of interest is. I studied Geology because I wanted to know about it. This whole career thing is doomed anyway. Radiology takes energy.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('jasonraymondson', '')$this->bbcode_second_pass_quote('PenultimateManStanding', 'Y')es, but you didn't say what your field of interest is. I studied Geology because I wanted to know about it. This whole career thing is doomed anyway. Radiology takes energy.