Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2013-06-30 20:23:13

the feral ipod
Novice

Offline

### 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

## #2 2013-06-30 20:38:13

bob bundy
Moderator

Offline

### 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

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

## #3 2013-06-30 20:46:28

anonimnystefy
Real Member

Offline

### 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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #4 2013-06-30 23:13:42

bobbym

Online

### Re: number substitution puzzle

Hi;

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #5 2013-07-01 04:14:54

the feral ipod
Novice

Offline

### 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,

## #6 2013-07-01 04:23:14

bobbym

Online

### 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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #7 2013-07-01 19:41:23

anonimnystefy
Real Member

Offline

### Re: number substitution puzzle

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #8 2013-07-01 19:56:55

bobbym

Online

### Re: number substitution puzzle

Hi;

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9 2013-07-02 01:04:13

anonimnystefy
Real Member

Offline

### Re: number substitution puzzle

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #10 2013-07-02 01:43:09

bobbym

Online

### Re: number substitution puzzle

Hi;

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.