Math Is Fun Forum

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Crossing the acid river

Here's the puzzle (sry but i don't know how to draw the diagram nicely):

There are 13 people stranded on one side of the acid river. Anyone that touches the river waters will immediately die. The river has stepping stones that are arranged something like this.
________
    0

0      0
   
    0     0

0      0

    0     0
------------
Only 3 planks are available to use. These planks can support any amount of weight. But the problem is, one plank can connect to the one horizontally(beside) to the other.

eg.

    0

0-----0
   
    0----0

0-----0

    0----0

And also if you connect two adjacent stepping stones , you can connect another nearest stepping stone with another plank.

eg. ________
    0

0-----0
   
    0----0
    |
0-+--0
         |
    0--+-0

Cross from bottom to top. Not left to right
How do all 13 people get to the other side of the river with only 3 planks?

Last edited by 1a2b3c2212 (2009-07-31 20:36:53)

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Crossing the acid river

Hi 1a2b3c2212,

I found a solution - here's an image of it that I drew up in MS Word.

I've colour-coded the planks and numbered their positions/repositions.

There are 2 options: Option A, which enables retrieval of only 1 plank once they've crossed, and Option B, which enables retrieval of 2 planks. Option A completes in 1 less move.

I couldn't find a way of retrieving all 3 planks.

Last edited by phrontister (2009-08-09 05:16:32)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Crossing the acid river

Hi phrontister;

I would give you an A just for the diagram!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Crossing the acid river

Hi, Bobby...

Thanks!

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

Last edited by phrontister (2009-08-09 20:47:14)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Crossing the acid river

thanks for the method of crossing. have any ideas how all 13 can cross in the shortest time? (that's the purpose actually =0 )

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Crossing the acid river

Hi 1a2b3c2212,

...have any ideas how all 13 can cross in the shortest time? (that's the purpose actually =0 )

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).

Last edited by phrontister (2009-08-12 00:48:12)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Crossing the acid river

what i meant was that should all 13 cross at 1 time or in groups? in reality the plank could squeeze up to 6 people.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Crossing the acid river

Oh, I see. That changes things considerably.

In your first post you said:

These planks can support any amount of weight.

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?

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Crossing the acid river

didn't specify so i guess it's allowed. but then i did it with my group, 2 min 02 sec. no piggy bag or pyramid. we're students lol not gymnasts.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Crossing the acid river

Hi 1a2b3c2212,

If the max number of persons on a plank at any one time is 6, then I reckon the minimum number of plank placements is as per my drawing B (ie, 11).

I'd split the 13 people into 2 groups of 6 + a single. So that the max limit of 6 per plank isn't exceeded, people from those groups, and the single, would at times have to occupy stepping stones (also occupied by one end of a plank) while the planks are moved into position (only one person per stepping stone is allowed, I presume). The planks would be passed from one person to the next as best suits the occasion and positioned in the order shown in the drawing.

I think the foremost planks and stepping stones should be populated as soon as possible.

I kept the Word file for my drawing B and moved objects around to find the optimum strategy, but I don't think I could illustrate that well in a single drawing...I'd have to do a series of them.

in reality the plank could squeeze up to 6 people.

I take it that doesn't include the part of a plank that rests on a stepping stone or another plank, otherwise I'm pretty sure it can't be done.

Last edited by phrontister (2009-08-15 20:50:41)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Crossing the acid river

you cracked the whole puzzle up! explained everything in my teacher's solution! gd job. that's practically the so-called strategy

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Crossing the acid river

Hi 1a2b3c2212,

that's practically the so-called strategy

Ah...thanks for that. You rescued me from trying to draw the solution in a series of steps, which wouldn't have been easy!

Your time of 2 min 02 sec is pretty impressive! Is that just for the physical crossing bit, or did that also include working out the strategy? If it's both, that sounds mighty incredible!!

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Re: Crossing the acid river

2min02 sec was our 4th try.. 1st try was like 5 min ++