Math Is Fun Forum

GK

Member

Registered: 2007-03-20

Posts: 6

Cube/Spider Problem Help..

Hi everyone..i really need the answer to this problem so i would really appreciate it if you help me..THANKS

A spider is standing on vertex (S) in this cube. (The cube's 8 vertices’ are (S,A,G,B,E,D,C,F)

(if you cant see the picture, click on the attached one)

The spider wants to walk to vertex (F), To get there it must follow these rules.
1. The spider can walk only along edges
2. The spider can walk along an edge, once only
3. The spider can only go down the vertical edges, never up
4. The spider can visit any vertex expect (F) more than once. When it gets to F, it must stop.
One way to get to F. is S-A-B-F...how many other ways can u find?
Please post the possible ways,too

tHANK U

Last edited by GK (2007-03-20 03:27:45)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Cube/Spider Problem Help..

My method is to use a tree diagram. I got 16 ways in all (including S–A–B–F). I might be wrong but I’m pretty sure that’s it.

GK

Member

Registered: 2007-03-20

Posts: 6

Re: Cube/Spider Problem Help..

My method is to use a tree diagram. I got 16 ways in all (including S–A–B–F). I might be wrong but I’m pretty sure that’s it.

Thanks, can you please post the ways...

thanks again

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Cube/Spider Problem Help..

Just use a tree diagram. From S, it can go to A, G or D. If A, it can go from it to B or E; from B it can go to G or F, etc. Exploring all the possible branches from S–A, you find there are 7 paths. S–G is exactly the same as S–A, so there are also 7 paths for S–G. And S–D is simple: it’s either S–D–E–F or S–D–C–F, just 2 ways.

GK

Member

Registered: 2007-03-20

Posts: 6

Re: Cube/Spider Problem Help..

Just use a tree diagram. From S, it can go to A, G or D. If A, it can go from it to B or E; from B it can go to G or F, etc. Exploring all the possible branches from S–A, you find there are 7 paths. S–G is exactly the same as S–A, so there are also 7 paths for S–G. And S–D is simple: it’s either S–D–E–F or S–D–C–F, just 2 ways.

im sorry but its kind of confusing..anyway
here are the ones I found (excluding S-A-B-F

1.    S-D-C-F
2.    S-G-C-F
3.    S-D-C-F
4.    S-A-E-F
5.    S-D-E-F
6.    S-G-B-F
7.    S-G-B-A-E-F
8.    S-A-B-G-C-F
9.    S-G-C-D-E-F
10.    S-A-E-D-C-F
11.    S-G-B-A-E-F
12.    S-G-B-A-E-D-C-F
13.    S-G-B-A-S-D-C-F
14.    S-A-B-G-S-D-C-F
15.   

whats the missing one ?
thanks alot

Last edited by GK (2007-03-20 03:51:54)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Cube/Spider Problem Help..

It would be so straightforward if you just used a tree diagram (which is what I keep saying).

You actually missed three (because you listed S–D–C–F and S–G–B–A–E–F twice). Two of them are S–A–B–G–C–D–E–F and S–A–B–G–S–D–E–F. The other is a path beginning with S–G – there should be 7 distinct S–G paths but you listed only 6 distinct ones. Check your S–G paths again.

Last edited by JaneFairfax (2007-03-20 04:33:32)

GK

Member

Registered: 2007-03-20

Posts: 6

Re: Cube/Spider Problem Help..

It would be so straightforward if you just used a tree diagram (which is what I keep saying).

You actually missed three (because you listed S–D–C–F and S–G–B–A–E–F twice). Two of them are S–A–B–G–C–D–E–F and S–A–B–G–S–D–E–F. The other is a path beginning with S–G – there should be 7 distinct S–G paths but you listed only 6 distinct ones. Check your S–G paths again.

thanks for ur time ..i guess thats it..right ?

1.    S-G-C-F
2.    S-G-B-F
3.    S-G-B-A-E-F
4.    S-G-C-D-E-F
5.    S-G-B-A-S-G-B-F
6.    S-G-B-A-S-G-C-F
7.    S-G-B-A-E-D-C-F
8.    S-G-B-A-S-D-C-F
9.    S-A-B-G-S-D-C-F
10.    S-A-B-G-C-D-E-F
11.    S-A-B-G-C-F
12.    S-A-E-D-C-F
13.    S-A-E-F
14.    S-D-C-F
15.    S-D-E-F

Maelwys

Member

Registered: 2007-02-02

Posts: 161

Re: Cube/Spider Problem Help..

It would be so straightforward if you just used a tree diagram (which is what I keep saying).

You actually missed three (because you listed S–D–C–F and S–G–B–A–E–F twice). Two of them are S–A–B–G–C–D–E–F and S–A–B–G–S–D–E–F. The other is a path beginning with S–G – there should be 7 distinct S–G paths but you listed only 6 distinct ones. Check your S–G paths again.

I used the tree diagram method as well (first creating a table of what points each point can link to, then a tree going through those possiblities) and I got 19 different answer. Haven't had a chance to double-check them against the diagram, but they all look like they should work...
[EDIT: Nevermind, now I'm at 14... somehow in building my relations chart I listed S-B as a valid connection, which obviously isn't true. Now I need to find where I'm missing stuff instead!]

Last edited by Maelwys (2007-03-20 05:10:49)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Cube/Spider Problem Help..

I get 16 paths as well. My way was to write out each path it could take along the top before dropping, then for each of those, write out each path it could take to F.

So, the paths along the top face are:

S (and SGBAS and SABGS)
SA (and SGBA)
SG (and SABG)
SAB (and SGB)

Dropping down to D, you can then either go EF or CF. There are 3 paths before you drop down to D, so that make 6 overall.

Dropping to E, you can go EF or EDCF. That means there are 4 paths that involve dropping to E.

Dropping to C is the same argument as dropping to E, but mirrored. So there are 4 paths again.

If you drop to F, then you're finished already. There are 2 paths on the top that finish at B, so there are 2 paths that drop to F.

Therefore, the total amount of paths are 6+4+4+2 = 16.

I might have missed a few somewhere though. I'd be interested to see Maelwys's other 3.

Edit: Ah, Maelwys edited. Never mind then.

Last edited by mathsyperson (2007-03-20 05:16:17)

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Why did the vector cross the road?
It wanted to be normal.

Maelwys

Member

Registered: 2007-02-02

Posts: 161

Re: Cube/Spider Problem Help..

Okay, I got it all straightened out now and ended up at 16 like everybody else. My other problem was that I'd misread rule #4 and thought that you could NOT repeat the same point twice, so I left out the paths that loop around the top and end up back at S before dropping. Apparantly I need to pay better attention. ;-)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Cube/Spider Problem Help..

1.    S-G-C-F
2.    S-G-B-F
3.    S-G-B-A-E-F
4.    S-G-C-D-E-F
5.    S-G-B-A-S-G-B-F
6.    S-G-B-A-S-G-C-F
7.    S-G-B-A-E-D-C-F
8.    S-G-B-A-S-D-C-F
9.    S-A-B-G-S-D-C-F
10.    S-A-B-G-C-D-E-F
11.    S-A-B-G-C-F
12.    S-A-E-D-C-F
13.    S-A-E-F
14.    S-D-C-F
15.    S-D-E-F

#5 and #6 are invalid paths – you are walking the edge SG twice.

I’ve already said before: there should be 7 paths beginning with S–G and 6 paths beginning with S–A excluding S–A–B–F. It doesn’t take much to count them and double-check your answers.

Last edited by JaneFairfax (2007-03-20 06:16:46)

GK

Member

Registered: 2007-03-20

Posts: 6

Re: Cube/Spider Problem Help..

1.    S-G-C-F
2.    S-G-B-F
3.    S-G-B-A-E-F
4.    S-G-C-D-E-F
5.    S-G-B-A-S-G-B-F
6.    S-G-B-A-S-G-C-F
7.    S-G-B-A-E-D-C-F
8.    S-G-B-A-S-D-C-F
9.    S-A-B-G-S-D-C-F
10.    S-A-B-G-C-D-E-F
11.    S-A-B-G-C-F
12.    S-A-E-D-C-F
13.    S-A-E-F
14.    S-D-C-F
15.    S-D-E-F

#5 and #6 are invalid paths – you are walking the edge SG twice.

I’ve already said before: there should be 7 paths beginning with S–G and 6 paths beginning with S–A excluding S–A–B–F. It doesn’t take much to count them and double-check your answers.

Good Lord. I'm totally lost ..please would you do me a favour and give me the right list.. thanks really..i'd really appreciate it

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: Cube/Spider Problem Help..

I've tried for an hour to find a shortcut ...no inspiation ,,,looks like the tree diagram is the final solution.

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Numbers are the essence of the Universe