Math Is Fun Forum

Hi Bobby,

I tried those exercises and I see what you mean. 1/10 surprised me.

I changed your code to run to 200 to avoid the endless looping. Btw, I don't know how to stop the program mid-stream - do you?

For terminated results LBASIC prints just the integer "200", but for non-terminations it prints "200.0". I suppose LB is saying that the number is not an integer, and that the number of zeros preceding other decimal digits exceeds its precision limit.

I tried that, but I got the same incorrect responses as before. Maybe I didn't code it correctly. I'll try again...

Re your first workaround:

As you suggested, I changed the offending line. I came up with:

Same results as before, in the same time.

Oh, I see. That changes things considerably.

In your first post you said:

I took that to mean each plank could support 13 people...but maybe the planks are too short for that.

Before I rethink, could you tell me if piggy-backing is allowed? What about human pyramids? Or must they stand on their own two feet?

Do you mean that there can only be up to 6 people on a plank at any one time?

Hi 1a2b3c2212,

The shortest I found is as per my diagram A, with 10 plank placements.

Is there a shorter method? If so, by how much? I think I'd like something to aim for.

Anyway, I like solution B, where 2 planks are saved. They could come in very handy: for instance, when the group comes to the narrow, 'uncrossable' giant poisonous (of course) stinging nettle patch, one of their adroit members can use the 2 planks as stilts, march across to the other side where the 13-man helicopter is and fly back to rescue the rest of the group...but (of course) there's only just enough fuel to get him back to the group (would you believe it!), and so he picks up the (very long) unbreakable rope that's laying on the ground by the helicopter, ties one end of it to the tree and puts the rest of the coil into the helicopter, allowing it to unravel as he flies off towards his mates; whereupon reaching them they ingeniously use their spare unbreakable rope (prudently saved from a previous adventure) to tie the planks (oh...did I forget to mention that he brought them back with him?) to the legs of the helicopter to act as skis, hook the rope up to the winch in the helicopter, climb aboard and winch themselves through the poisonous nettles to the safety of the other side...where lies a terribly-treacherous tributary of the Acid River that can only be crossed with 2 planks!!

I'll have another look at my solution to see if I can shorten it.

Nice puzzle, by the way. I've enjoyed having a go at it (I was going to say "solving it", but it looks like I've still got work to do on it).

Hi Bobby,

Thanks for all of that! I could only look at it quickly this a.m. and I've got to run now, so I'll have a closer look at it tonight. 

The principle of this workaround came to me in bed last night just before I went to sleep (my mind's most productive moments!), and I was going to post about it morning...but you've saved me the trouble.:)

I'd already uninstalled GhostScript, Bobby, as I nearly never have to read .ps files. I can't see that I'd have much use for djvu or puppy, either.

I use PDF-XChange Viewer for pdf, as it has a few annotation tools that I find handy.

I was curious to find out how an experienced BASIC programmer would tackle this in BASIC, and as I use LibertyBASIC I posted a question on their forum this afternoon. Janet responded (verrrrry quickly!) with this code, which in 86 seconds finds that there is only one solution (the one quoted by Bobby...plus its 5 positional permutations):-

I haven't tried to understand the code yet, but I'll post it now anyway.

Thanks, Bobby.

I downloaded Vardi's article. Most of the internet links I could find were to .ps files, for which it seems I need to install a reader my computer doesn't have. I found a .pdf file at:-
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=35990630E61962A0BE5D8EDD171CB9B1?doi=10.1.1.33.4288&rep=rep1&type=pdf

I read the article, but the explanation to the part 2 solution, in particular, is way beyond my grasp and confirms that I'm doomed to limiting my experience with the cattle problem to part 1.

For part 1 Vardi mentions using Mathematica and gives the final equations for use with that program's Solve command. Again - too advanced for me.

My solution to part 1 is a simple, step-by-step algebraic one...which I'll post when I've set it out sufficiently well. Maybe others might like to try this non-computer approach in the meantime.

Hi Bobby,

If you have time, could you post the code for solving this in BASIC? That's the only language I 'know' atm - I'm hoping to venture into something else some day when I get some spare(!) time...maybe Python.

I've had a fair sort of a crack at it but am not getting anywhere with it because I haven't done much programming, and I'd like to learn. If I wrote the code myself I'm sure that running it would melt my cpu.

Thanks!

Hi, Bobby...

Thanks!

I'll pass on your compliment to M$ Word's programmers.

eschewed

yet

Here's an image of the Excel worksheet that I used for testing my formula on the first 30 groups.