Word Problem

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mjtnas

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Feb 7, 2010
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I have been trying for three weeks to solve the word/photo problem in the attached document. PLEASE Help...its my last one! Thank you!!

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3 weeks? Can you show me some work so I can see where your problem is? Label them first off and come up with a system to explain moves (simply). i.e train, car A and car B, and I see 6 positions.
 
I keep getting lost in the trial and error. Even my math tutor is having problems with this one....go figure. I've labeled and moved them, got out props and all. I just always end up with the locomotive stuck between the two cars.

Its been a long time since I've done math and I've been very ill so I'm a bit foggy. It's probably plain as day but I don't see it.
 
Ok, this is not trial and error. So throw that out of the window. You need to assume that the cars can be left on the straight lines to the left of the circle.

Ok, label everything

T = locomotive
A = car A
B = car B

and then label the positions starting from the top left of the diagram. P1, P2, P3, P4, P5, P6

P1 = being where the locomotive (T) is now. (Upper left straightaway)
P2 = being where car A is
P3 = tunnel
P4 = where car B is
P5 = lower left straightaway
P6 = curve opposite the tunnel

Now you can describe everything.

T takes A goes to P4 and takes B. So ATB at P4

go straight to P5 and leave A, TB to P5

TB to P2, TB turns to BT, BT to P1, leave B at P1

Can you take it from here?
 
I usually get this far and get my train stuck between the two. I'll try a few more times.
 
That was just an example, There are multiple ways to do it, but you'd want the most efficient.

Hint: get A to P1 and B to P5. (even though you may not have to)

If you can't see it forwards, work backwards from the finished position. That's a perfectly fine approach.
 
from B@P1 and A@P5

B to P6, circle around, A to P6. BAT@P6

BAT to P4, BAT to P5, leave B@P5
 
Ooh, it took me 13 moves to swap A with B and to put T back at P1.

That didn't feel very efficient. :(
 
Re:

mmm4444bot said:
Ooh, it took me 13 moves to swap A with B and to put T back at P1.

That didn't feel very efficient. :(
Click to expand...

yeah, I didn't count mine, but it was a lot. It's a hard problem
 
tutor_joel said:
It's a hard problem Yes, it was more challenging than I expected.
Click to expand...

I took your advice, and thought about how the last few steps would need to go.

Clearly, it would be nice to have B-T-A @ P4, because A could be dumped right where it needs to be, and then B-T rolling clockwise to P2 would become T-B, where B could be dumped right where it needs to be, allowing T to return to P1.

It took me 11 steps to get B-T-A @ P4, working from the beginning.
 
I tried before I saw these subsequent posts and ended up with this...

First, I redrew the track on a large piece of paper and labelled everything.

T = locomotive
A = car A
B = car B

Next, I labeled the positions starting from the top left of the diagram. P1, P2, P3, P4, P5, P6

P1 = the starting location of the locomotive (T) (upper left straightaway).
P2 = the starting location of car A at the top
P3 = tunnel
P4 = the starting location of car B at the bottom
P5 = lower left straightaway
P6 = curve opposite the tunnel

Next I used trial and error and ended with the following sequence:

T moves to P4 and creates TA
TA moves to P5 and leaves A
T backs up and moves through P6 then through P2 and through P3 and stops at P4
T becomes BT
BT moves to P5 where A is still resting and becomes ABT
ABT backs up and moves to P2 and becomes TBA
TB leaves A at P2
TB moves back to P4 and becomes BT
BT moves back to P5 and leaves B
T then moves through P4, through P3, and stops at P2 where A is still resting becoming AT
AT moves to P4 and becomes TA
T leaves A at P4
T moves to P5 where B is still resting and becomes BT
BT backs up to P4
BT moves to P2 and comes TB
T leaves B at P2 and returns to P1
 
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