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#1 2013-09-29 06:40:58

jacks
Member
Registered: 2012-11-21
Posts: 80

counting problem to spell MATH

Starting at the M in the center of the Letter below, you may move Left, Right,Up or Down to anadjoining Letter.

How many Distinct paths can be followed to spell the word MATH

View Image: MATHCOUNT.jpg

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#2 2013-09-29 07:04:29

jacks
Member
Registered: 2012-11-21
Posts: 80

Re: counting problem to spell MATH

I am Getting 12. To Admin. (bobbym) is it right or not

Thanks

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#3 2013-09-29 07:07:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: counting problem to spell MATH

I do not know yet, I have not worked on the problem. I am busy with the other ones.

But a cursory examination yields at least 16 so I would think 12 is incorrect.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#4 2013-09-29 08:39:44

Au101
Member
Registered: 2010-12-01
Posts: 286

Re: counting problem to spell MATH

I got twelve by following it round, almost as if it were a clock, but then I noticed that there are other ways (e.g. left, up, left). I'm sure there's a way to be sure (this isn't really my area of expertise) but just a cursory attempt at a brute force solution seems to suggest to me that 16's a pretty good answer.

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#5 2013-09-29 09:22:47

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,391

Re: counting problem to spell MATH

hi jacks

Draw the grid and letters and write a 1 over the M.  There's only one M so all routes start there.

Now go to an A.  There are 4 of these so write a 1 over each.  (see picture)

Now to go to a T.  I've just shown the ways to get to one of the Ts.  You can go up then right, or right then up so I've written a 2 over that T.  Do the same for the other Ts.

Now how can you get to an H from a T?  Work that out and write the correct number over each H.  Add them up and there's your answer.

EDIT:  I'm getting a lot more than 16.

Bob

View Image: jacks5.gif

Last edited by bob bundy (2013-09-29 09:31:20)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2013-09-30 06:59:22

jacks
Member
Registered: 2012-11-21
Posts: 80

Re: counting problem to spell MATH

Thanks bobbundy I am Getting 28

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#7 2013-09-30 07:05:36

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: counting problem to spell MATH

Hi jacks

I'd say 28 is correct.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#8 2013-09-30 07:10:06

jacks
Member
Registered: 2012-11-21
Posts: 80

Re: counting problem to spell MATH

Thanks  anonimnystefy

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#9 2013-09-30 07:22:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: counting problem to spell MATH

If anybody is interested, my method is:

I looked at the upper left-hand side only.
      H
    HT
  HTA
HTAM

In this part, there are 2^3 paths which produce MATH, because, at every letter we can either go up or right, and there are 3 places where we make the choice.
It's the same for the other 3, so it's 32 total, but, because we counted each straight path twice, we subtract 4 to get the number of possible ways to spell MATH to be 28.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#10 2013-09-30 09:53:09

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,391

Re: counting problem to spell MATH

hi

I think 28 too.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#11 2013-09-30 10:02:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: counting problem to spell MATH

I like it when my answer agrees with somebody else's. smile


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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