P&C q8
- Thread starter Saumyojit
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pka
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The ant must move five places
How many ways can we arrange the string [MATH]RRRRRUUU~?[/MATH]
so the ant is facing towards up starting his journey, not towards right?
After taking 5 rights he now faces towards right .So to left is B he takes 3 steps.
how do i decide which side the ant faces after taking every step
pka
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The ant could change its mind and start off to the right right.
Dr.Peterson
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Just try a few possible paths in order to discover the requirements for a shortest path. Show us your pictures. We're all familiar with this sort of problem, so we can start already knowing how it works. You need to see it for yourself. So that's all the hint I can give.
Which direction it faces is irrelevant; all that matters is the direction of movement on each step.
Yes i did some possible steps.
Right , up or left , right, up or left , right ,up or left, right, right
Another maybe ,
Right , up or left , up or left , right ,right ,up or left, right, right
(Right , up or left , right, up or left , right ,up or left, right, right) Given in the image
For all of this arrangements , the problem demands that I assume the ant is Facing upwards before starting it's journey .
I have given or as after ant takes the first right and reaches the second point , now he has to go to 3rd point if it faces towards right then it has to take left OR if it faces upwards , then it has to go up to go to 3rd point.
This is the confusion and i hope i am able to explain to you .
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Dr.Peterson
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Did you not find that if you go right and then left, you go farther than if you always go either right or up? That's what I expected you to realize.
In the image, it never goes left. I wonder if you are thinking that right and left refer to the direction of turning, rather than motion? It's intended to mean the latter. Your image consists of only right and up motions, so it is one of the shortest possible routes you are to count.
As I said, the problem has absolutely nothing to do with the direction it is facing, or with turning. The problem could just as well have been stated in terms of sliding a pawn along the grid. Do you understand that? It is just sitting there at the start, and can be moved either up or right from location A.
So, as Jomo said in #3, any shortest path can be described as a permutation of RRRRRUUU. Your example is RURURURR.
pka
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To Sauyojit, the number of ways to arrange the string [MATH]RRRRRUUU[/MATH] is [MATH]\dfrac{8!}{5!\cdot 3!}=56[/MATH].
Cubist
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@Saumyojit I agree with you that the manouvre of going "right then up" from a top-down view perspective is the same as:- " I am the ant within the maze. I initially face directly towards row 1. I turn right and walk forward, then I turn left and walk forward."
However, I recommend that you ONLY think of this as if you're a person watching the ant, viewing the scene from above. Otherwise it will be very confusing if you switch perspectives.
However, I recommend that you ONLY think of this as if you're a person watching the ant, viewing the scene from above. Otherwise it will be very confusing if you switch perspectives.