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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: 90,615

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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: 6,531

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: 15,657

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: 15,657

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: 6,531

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: 15,657

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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