real cunundrums

[matt000r000]

things that don't realy fall anywhere in mathmatics

 

[stapel]

things that don't realy fall anywhere in mathmatics

I'm sorry, but I don't understand what this exercise is saying...? Is there any other information available?

Thank you!

 

[matt000r000]

1st big cunundrum:

i am working on programing my calculator, but it doesn't have character support. aka, i can't type words into it and expect an answer, since the letters are used as variables. so, i decided to create my own support. since the letters are variables, puting them next to each other multiplies them. i thought long and hard, and figured out the following: in order to work, i need 26 values such that multiplying any two, three, or four will produce a unique value. thats where the math comes in. i need 26 values, one for each letter, so forming a word will result in a unique number, so then the calculator can understand and compute words! i will post any progress i make on this problem. any help whatsoever is greatly appreciated!!!!!

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"if you can't fly, run. if you can't run, walk. if you can't walk, crawl, but by all means keep moving!"
-Marthin Luther King, Jr.

P.S.
-the first post in the category was just to further explain the purpose of the category.

 

[daon]

What about tac and cat? Two words with the same value when multiplied.

You'll need to use powers of 26 to distinguish between words. That is, use BASE 26. tac and cat are two unique decimal numbers in base 26.

tac = t*26^2 + a*26 + c
cat = c*26^2 + a*26 + t

 

[matt000r000]

ah, but this is how my calculator works:

set a variable, say "t", "a", and "c", as set numbers, say 1, 2, and 3. then, typing "tac" on the screen, the calc would see:

t x a x c
1 x 2 x 3
6

and it would return "6". that would be a good idea what you're saying, but it isn't an option to me. by the way, i'm assuming letter order doesn't matter, or can be found in the context. for example, a word un-scrambler doesn't need to know letter order, but only the letters involved.

 

[matt000r000]

2nd big conundrum

here's my seccond big conondrum:
how do you express |x| using only + - x \ ^ symbols? (note: powers must be integers and there is no square root!) i need to know this again for programing, exept this time its on the computer. can you help me? any help whatsoever is greatly appreciated!

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"if you can't fly, run. if you can't run, walk. if you can't walk, crawl, but by all means keep moving!"
-marthin luther king, jr.

 

[daon]

I'm not sure I get what you mean.

You don't care if you type "crap" and it returns "carp?" The values won;t be unique is what I'm saying.

Another problem that might arise is two completely different words returning the same value. i..e if a = 1, b=3, e=2, d=5, f=10 then

bead = 3*2*1*5 = 30

fab = 10*1*3 = 30

To get around this, you need to either do what I mentioned above with powers of 26 or use primes only. Assign each letter a prime number.

a = 2
b = 3
c = 5
d = 7
e = 11
...etc

Then, at least, you'll return words with the same letters, and the same number of letters. i.e. if you type in "dead" (7*11*2*7 = 1078) your program will know your word has exactly 2 d's, 1 a, and 1 e. This is due to the fundamental theorem of arithmetic.

Using the powers of 26, you'll know the EXACT word. each time you divide your number by 26, you'll get the exact last letter of the remaining word.

Say a=1, b=2, c=3, ..., z=26=0.

Then "cab" = 3*26^2 + 1*26 + 2 = 2056.

Now to get "cab" back from 2056:

1) DIVIDE BY 26. 2056 / 26 = 79 R2.

That R2 ("remainder = 2") corresponds to the last letter. 2 = b.

2) Divide 79 by 26: 79/26 = 3 + R1

R1 implies the second letter = a.

3)Finally, your left with 3. That means the first letter was c.

.......

I'm not sure what you mean by expressing |x| as an algebraic expression. |x| = max{x, -x} if x is a real number. You can also compute it by SQRT(x^2} but you said no square roots.

 

[matt000r000]

thanx for the prime idea. it realy helps. by the way, i was saying the word order doesn't matter, just what letters are in it. for example, i could ask for a number in word form, and the possible answers would be:
one
two
three
etc..
so, in the context of the question, knowing that 2 'n's, a 'i', and an 'e' constitutes the answer "nine". and, for the seccond time, i CANNOT DO THE POWERS OF 26!!!!!!!!!!!!! MY CALCULATOR CANNOT DO THAT AND ACTUALY LOOK LIKE A WORD!!!!!! if i did do something like that, instead of typing in

CAT

i would have to type in

C*26^2+A*26+B

which simply defeats the whole purpose. it would be easier to ask for the letters individually.

and thanx for your help in the seccond cunundrum. i said "only using: + - x / ^". so i couldn't do that "max{x,-x}" thing, and, yes, i said no square roots, otherwise it would be as easy as that.

 

[Denis]

for example, i could ask for a number in word form, and the possible answers would be:
one
two
three
etc..

Matt, whatever you're trying to do (I still have no idea what it is!), you're apparently trying to do it to a
"calculator"...WHY?
Are you a student attending math classes, or someone just interested in maths?
If you're trying to have fun programming, why don't you download a programming language
(like UBasic), then program with none of the restrictions of a calculator?

 

[matt000r000]

to answer your question, i am someone who has fun doing mathmatics. and, yes, i am programming my TI-83+. and, yes, i do have c++ visual basic. the calculator simply helps me in school. i was just trying to make it more user-freindly, for i program my freind's calculators for them. and my problems have been answered, thank you!

 

[DrMike]

Re: 2nd big conundrum

how do you express |x| using only + - x \ ^ symbols?

This almost works :

(x^((x+x)/x))^(x/(x+x))

 

[daon]

Re: 2nd big conundrum

how do you express |x| using only + - x \ ^ symbols?

This almost works :

(x^((x+x)/x))^(x/(x+x))

If you're going that far then you might as well circumvent a square root symbol with a rational power.