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## #1 2013-06-29 22:23:13

the feral ipod
Member
Registered: 2013-06-29
Posts: 2

### number substitution puzzle

Hi all, I am new!

Some 50 years ago I made a puzzle as follows.

Given that characters take unique positive integer values, add together the three words below to give tha answer

force
feet
secs
power

given that there is no zero, what are the characters values.

Recently I "think" I found this puzzle somewhere unexpected, has is spread in all those years or did someone else create it independantly, quite likely really.

I would like to hear fromany oone with an HONEST statement of how long it takes to solve, it took me a LONG time back in them early 60's!

Best wishes

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## #2 2013-06-29 22:38:13

bob bundy
Registered: 2010-06-20
Posts: 8,354

### Re: number substitution puzzle

hi the feral ipod

Welcome to the forum.

That puzzle looks interesting but I won't start until later as I'm just taking a short break from clearing out a room right now.

Just to be clear :  Are we looking for a 5 digit number + a 4 digit number + a 4 digit number = a 5 digit number  ?  (ie. each letter represents a single digit {1,2,3,4,5,6,7,8,9}  )

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2013-06-29 22:46:28

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: number substitution puzzle

I think he means that.

add together the three words below

I am assuming he wants the first three words summed to get the fourth.

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
The knowledge of some things as a function of age is a delta function.

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## #4 2013-06-30 01:13:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: number substitution puzzle

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2013-06-30 06:14:54

the feral ipod
Member
Registered: 2013-06-29
Posts: 2

### Re: number substitution puzzle

Thanks for that,

My Math is, (was) at degree level and my programing skills have been professional in the past but I would love to see an algorithm for this class of puzzle, as well as a manual process!

My question was, however, has anyone seen this particular puzzle in the public domain?

Thanks and best wishes,

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## #6 2013-06-30 06:23:14

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: number substitution puzzle

Yes, they are common but they are rarely solved on math forums, They are called alphametics or cryptarithms.

The algorithms range from brute force to implementing the same tricks a human problem solver uses. There are some fairly obvious moves.

For modern machines brute force does well on this small problem. No matter how tough the problem is you always have less than 10! possibilities. Even using a slow language that will not take very long.

For instance this is the toughest one I worked on

NINETYNINENONILLIONNINETYNINETRILLIONNINETYONE = NINETYNINENONILLIONNINETYNINETRILLIONFORTYFIVE + NINETEEN + ELEVEN + TEN + FIVE + ONE.

it went down to a brute force attack.

Canonically, I don't know of any 'short cuts' for problems such as this. In general it's just trial-and-error along with some deductive elimination and a lot of branch-and-bound search.

As for a math way? I tend to doubt that math is the right tool here. You can play around with diophantine equations or generating functions or both but it still looks like a programming task rather than a mathematical one.

Here are pages that host lots of problems.

http://www.mathematik.uni-bielefeld.de/ … LPHAMETIC/

http://www1.maths.leeds.ac.uk/~pmt6jrp/ … metic.html

Some hints on how to do them if you want to do them by hand or maybe write a smart program.

http://everydaylearning.handinhandhomes … phametics/

http://www.tkcs-collins.com/truman/alph … olve.shtml

Solve some:

http://cryptarithms.awardspace.us/solver.html

Robert Israel's page on them provides some advice and an app to solve them.

http://www.math.ubc.ca/~israel/applet/metic/metic.html

Google using the two words given above and you will probably come up with a web app and a downloadable app to do them.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #7 2013-06-30 21:41:23

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: number substitution puzzle

NINETYNINENONILLIONNINETYNINETRILLIONNINETYONE = NINETYNINENONILLIONNINETYNINETRILLIONFORTYFIVE + NINETEEN + ELEVEN + TEN + FIVE + ONE.

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
The knowledge of some things as a function of age is a delta function.

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## #8 2013-06-30 21:56:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: number substitution puzzle

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #9 2013-07-01 03:04:13

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: number substitution puzzle

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
The knowledge of some things as a function of age is a delta function.

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## #10 2013-07-01 03:43:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: number substitution puzzle

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline