Math Is Fun Forum

Hi thickhead;

That is a trickily worded question!

Still wrestling with the wording, though...

Hi;

Here's a graphic solution:

Oh...I overlooked that.

I think your answer is right, but I haven't checked your method yet. Gotta go out now for a couple of hours at least, and I'll look at it again later.

Thanks for clearing that up for me, thickhead...I hadn't been able to find out any information about that anywhere.

Btw, I think that in your previous post you meant PQT for the altitude, not PQR (as per the question)...but the answer would be the same.

Hi Bob,

Sorry, I didn't mean to correct you where there was no need, but you did throw me earlier by saying that you'd improved your diagram by making it accurately to scale, and I hadn't understood what you meant by that.

Hi Bob & math9maniac;

I get a different shape from Bob's, which seems to have PQ=approx 25 instead of 20.

Also, I think I recall from school that the apex of a triangle in relation to its height is denoted by the middle letter (same as for an angle). If that's right, then "the height of triangle PQT" would be QB in my drawing.

Hi Bobby,

My code covers the range of 1 to 15 seats, but I'll concentrate just on the 15 seats option, for which the code would be:

Count[StringFreeQ[Map[StringJoin,Tuples[{"m", "w", "k"},{15}]],{"ww","mmm"}],True]

There are 14348907 tuples, ranging from "mmmmmmmmmmmmmmm" through "wwwwwwwwwwwwwww" to "kkkkkkkkkkkkkkk".

StringJoin maps over Tuples to concatenate the comma-delimited tuples format to make it easier for me to work with.
StringFreeQ yields "False" for any items that contain either "ww" or "mmm", and "True" for any that don't.
Count yields the total number of "True" results...which is 2291229 (Anna's answer, and my Excel's).

A search through the 14348907 tuples for the valid maximum arrangements you mentioned found 640 (ie, 5(2^7)) for 10 men and 128 (ie, 2^7) for 8 women.

Here's one example of each:

Men: {mmkmmwmmwmmkmmk}...position 1083351.
Women: {wmwmwkwkwmwkwmw}...position 5424635.

------------------------------------------------------------------------------------------------------------------
I haven't been able to work out how to create a list of the 2291229 valid arrangements. StringFreeQ only yields "True" or "False", and I can't get any more info from it than that. I've tried other functions (eg, Cases, DeleteCases, Select), but I must be doing it wrong. Not knowing much about patterns probably doesn't help.

So, the "search through the 14348907 tuples" I mentioned above was through Excel, which I trust as being as correct as M's results because they're identical for all 1 to 15 levels...and my M code is based on my Excel method. Also, I found the 1083351 and 5424635 positions with Notepad++ from a csv file I created with M of the 14348907 tuples.

Could you help me with creating the list in M of the 2291229 valid arrangements, please? I've tried and tried, but am totally stuck. Thanks!

So far I've got this to work:

EDIT: Found something on SE that works, and prints all 2291229 solutions:

Not yet. I've tried again, but still can't get past a major obstacle that's holding up progress. I may need your help with that, but I'll give it another go first.

Hi all;

I hope my logic's ok.

Here's an example copy of my 3-column spreadsheet layout that shows what I did. I used the 5-seat option to keep the list to a manageable size.

Column B is M's copy/paste output of all 243 permutations for 5 seats.
Column A tests column B entries for either a "ww" or "mmm" content, and identifies, via incremental numbering, all valid seating arrangements.
Column C's first cell displays column A's last number.

The other seating numbers options use this same method.

EDIT: I've since changed column A's code, as evaluation for >10 seats was unacceptably slooooow. This means that the incremental numbering is no longer reported there - only "TRUE" or "FALSE". That also meant changing C1's code, but the totals remain unchanged.

Hi Enshrouded_;

1. Does this help...?

Hi Calligar;

I can't access the movie from your link, because I get this error: "Sorry, this video is not available in your region due to licensing restrictions." My region is Australia.

There's an English dubbed version on YouTube here, and the puzzle appears at 5:38.

Btw, re the hide box (etc), you can always see how other posters have done it by clicking the 'Quote' button in the bottom right-hand corner of a post...but only if you're logged in.

Oo...didn't know that one!