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kevincan
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See attached plan The map ATTACHED shows Linas Updated on: 12 Jul 2006, 16:48
Originally posted by kevincan on 09 Jul 2006, 03:28.
Last edited by kevincan on 12 Jul 2006, 16:48, edited 1 time in total.
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The map ATTACHED shows Lina’s neighbourhood. The streets and avenues are laid out so that it takes Lina exactly one minute to walk from one street or avenue to the next. Lina wishes to go on an 8-minute walk from her house to Sarah’s office. If Lina is allowed to choose any route so long as she does not go off the grid shown, how many routes does she have to choose from?



(A) 448 (B) 450 (C) 452 (D) 454 (E) 456



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See attached plan The map ATTACHED shows Linas 11 Jul 2006, 15:01
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Hint: How many distinguishable permuations of the letters of "mississippi" are there?
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See attached plan The map ATTACHED shows Linas 11 Jul 2006, 22:05
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See attached plan The map ATTACHED shows Linas 12 Jul 2006, 13:44
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I would like to know the answer and the way to figure it? Could't figure it, doesn't seem to be as simple as finding the no: of permutations of letters in 'MISSISSIPPI' though!

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Would it be much easier if it were 6 minutes instead of 8?
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from your original sketch, we know that there are 8 streets that we can not take in order to get to Sarah's house within 8 minutes. Please see attached file.

Also, I know that I have to be within the blue lines, but within the blue lines, there are going to be paths that are not going to work since I have to get to Sarah's house with in 8 minutes.

I have counted the number of horizontal lines (1minute) in the attached file, I have only numbered 1,2,3, and 4. But there are a total of 26 horizontal lines and a total of 24 vertical lines.

This totals to 50 possible lines that I can use in groups of 8 (8minute) to get to Sarah's house. I feel so close, yet so far...
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If she wanted a six minute walk she would need to move up (U) twice and right (R) four times
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Isn't the number of ways 448, is it?
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See attached plan The map ATTACHED shows Linas 12 Jul 2006, 16:50
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You're right- sorry for the typo! Did it take a long time to solve?

Congratulations!
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thank you

well, now that I remember my combinatoric course ....

pretty tough question
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game over
Isn't the number of ways 448, is it?
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if you don't mind, can you please explain your work?
thanks
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See attached plan The map ATTACHED shows Linas 12 Jul 2006, 18:36
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We know Lina wants to take an 8 minute walk. So she would have to move 8 'clicks' up or to the right.

There are several ways to do it:

One is move left once, right 5 times, and up once. So if write a word, we get:
LRRRRRUU --> # of permutations = 8!/5!2! = 168

Another way is
Down once, right 4 times, up 3 times, writing it into a word, we get:
DRRRRUUU --> # of permutations = 8!/4!3! = 280

Total number of ways = 168+280 = 448
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ywilfred
We know Lina wants to take an 8 minute walk. So she would have to move 8 'clicks' up, down, to the left or to the right. The net result must be 4 to the right and 2 up.

There are several ways to do it:

One is move left once, right 5 times, and up twice. So if write a word, we get:
LRRRRRUU --> # of permutations = 8!/5!2! = 168

Another way is
Down once, right 4 times, up 3 times, writing it into a word, we get:
DRRRRUUU --> # of permutations = 8!/4!3! = 280

Total number of ways = 168+280 = 448
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Excellent, I've made a couple of changes to make your solution the OE!



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