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

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**

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

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

Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,735

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

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

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

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

Thanks bobbundy I am Getting 28

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

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

Thanks anonimnystefy

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi

I think 28 too.

Bob

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

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

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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