Math Is Fun Forum

Hey!

Hey (:

The values are correct. Once I switched to Excel everything matched (up to 12 seats so far). I will do the rest later and attempt general rules. Also keeping track of the numbers of adjacent and multiple adjacent combinations.

Good to finally have a reliable count.

Hi bobbym,

The only difference between the forms in post #2 and #1 is that #2 is continuous at x=0.

Thank you for bringing integer relation algorithms to my attention!

It has honestly never occurred to me before that there might be numbers that can't be expressed in terms of known constants. It sounded counter-intuitive to me, until I realised that it does not imply that there are numbers which cannot be expressed in terms of defined operations. It merely means that it is sometimes necessary to expand our collection of "known constants".

It does not have to be done by hand, but I would like to know something about the two analytical forms (or determining that they cannot be found). If you cannot find them, can you elaborate on how this might be investigated?

It is not a practical problem since it is relatively easy to approximate the answers to a desired degree. I am just curious (and pedantic)

Hi

Hey!

From all of the new formulas, the updated general formula for the answer in terms of n seats is:

The updated answer for n=15:

And we are as far as ever from an intuitive explanation

Oh my gosh, you are correct. 21 is definitely right. But I haven't the faintest why the darn thing isn't picking those up.

*,w,w,* fails to search w,*,w,w. How... irritating

Similarly 5 seats is missing
{w,k,k,w,w}
{w,k,m,w,w}
{w,k,w,w,k}
{w,k,w,w,m}
{w,k,w,w,w}
{w,m,k,w,w}
{w,m,m,w,w}
{w,m,w,w,k}
{w,m,w,w,m}
{w,m,w,w,w}

so the right number is 75 instead of 65...

The problem is not too difficult to overcome, however. I will list the numbers of combinations of w,*,w,w as well as the numbers of duplicates between w,*,w,w and *,w,w,* shortly. All we have to do is add the first and subtract the second from our given numbers and general rule. Since the result then agrees so far with manual and exhaustive listing, this should be the only quirk.

Hey (:

Hi (:

The list does include {w,w,w,m} and {w,w,w,w} in the 9th and 10th rows.
I used "pattern *,w,w,*" for this.
"pattern *,m,m,m,*" for the males,
and both for both.