how many can be formed?

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Jivago

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How many words using these rules can we get?

26 letters

y is a vowel here : rhythm , syzygy etc ...

w is a vowel too here : wppwrmwste (an obsolete spelling of uppermost)

thus vowels : a e i o u y w

minimum of letters for a word : 2 ( needs a vowel )

maximum of letters for a word 29

max of consonants in a row : 6 ( but the same can't be repeated consecutively more than twice = ss ttt mmm bbbb etc .. but if interwoven it is ok : archchronicler , schylds , wppwrmwste etc )

max of vowels in a row : 5 ( but the same can't be repeated consecutively more than twice = aaa iiii uuuuu etc .. but if interwoven it is ok : queueing etc )

I wonder how many words we can form using these rules ... please show the equations too . THANKS : )
 
Hello,
Please read the guidelines for the forum which basically says that we will not solve any problems for a student as we want the student to solve the problem on their own with our helpful hints. So please read the guidelines, follow them and then post back. Most importantly show us the work you have done so far so we know where you need help.
 
I don't know how to solve it ... I know nothing of math ... :cry::cry::cry:

Can someone show me the ''formula'' to solve such a complex equation?
 
Jivago said:
I don't know how to solve it ... I know nothing of math ... :cry::cry::cry:

Can someone show me the ''formula'' to solve such a complex equation?
Click to expand...
"... I know nothing of math ..."

Then why are you "wrestling" with this problem??
 
Well, you got our attention three times. How's that going for you? If you would like to learn something, show us what you have to start with (which, by definition, is more than nothing) and we'll be happy to help. Being demanding and otherwise noncommunicative will not get you very far.
 
I need this ? .. but I don't know even where to start ... ?

How many words using these rules can we get?

26 letters

y is a vowel here : rhythm , syzygy etc ...

w is a vowel too here : wppwrmwste (an obsolete spelling of uppermost)

thus vowels : a e i o u y w

minimum of letters for a word : 2 ( needs a vowel )

maximum of letters for a word 29

max of consonants in a row : 6 ( but the same can't be repeated consecutively more than twice = ss ttt mmm bbbb etc .. but if interwoven it is ok : archchronicler , schylds , wppwrmwste etc )

max of vowels in a row : 5 ( but the same can't be repeated consecutively more than twice = aaa iiii uuuuu etc .. but if interwoven it is ok : queueing etc )
 
Can you write down some allowable words? How are you determine that they are allowable?

BTW, not all math problems have a formula. Some problems require some thought and then the solution comes naturally w/o a formula! You have to try.
 
Jivago said:
How many words using these rules can we get?
26 letters
y is a vowel here : rhythm , syzygy etc ...
w is a vowel too here : wppwrmwste (an obsolete spelling of uppermost)
thus vowels : a e i o u y w
minimum of letters for a word : 2 ( needs a vowel )
maximum of letters for a word 29
max of consonants in a row : 6 ( but the same can't be repeated consecutively more than twice = ss ttt mmm bbbb etc .. but if interwoven it is ok : archchronicler , schylds , wppwrmwste etc )
max of vowels in a row : 5 ( but the same can't be repeated consecutively more than twice = aaa iiii uuuuu etc .. but if interwoven it is ok : queueing etc )I wonder how many words we can form using these rules ... please show the equations too . THANKS : )
Click to expand...
You have posted that you really need this solved. In that case if I were you I would hire a good programmer to solve this. Frankly I find your writing almost impossible to follow. It is so filled with inclusions and exclusions, with converses and inverses. This is a finite, closed problem it is possible to list all strings of the alphabet of length two to twenty-nine. Once list is made, it is possible to check each for the required conditions. But that is a job for a computer. Although I at one time made extra money doing something similar usually for education theses I would even try this one.
 
Jomo said:
Can you write down some allowable words? How are you determine that they are allowable?

BTW, not all math problems have a formula. Some problems require some thought and then the solution comes naturally w/o a formula! You have to try.
Click to expand...
well I haven't thought about that .. I guess all combinations ... ...
 
pka said:
You have posted that you really need this solved. In that case if I were you I would hire a good programmer to solve this. Frankly I find your writing almost impossible to follow. It is so filled with inclusions and exclusions, with converses and inverses. This is a finite, closed problem it is possible to list all strings of the alphabet of length two to twenty-nine. Once list is made, it is possible to check each for the required conditions. But that is a job for a computer. Although I at one time made extra money doing something similar usually for education theses I would even try this one.
Click to expand...
wow .. so this is really a hard problem to solve o_O ... my quest is to find how many words we could make using the alphabet ... from 2 letters up to 29 ... and I made those rules so that we don't have words like ttttt trffkpp mmbbvvv etc etc :(
 
Jivago said:
well I haven't thought about that .. I guess all combinations ... ...
Click to expand...
How can it be all combinations if there are restrictions. You are not trying at all and here is why--I asked if you could write down some allowable words and you basically said that you did not know of any, yet in your original post you listed some.

If you are not going to try at all then stop bothering us with this. This is a help forum not a math problem solving service. You in the end if you want us to help you with this problem will solve it, not us. I have been on this forum for over 5 years and I have yet to solve one problem for a student and I am certainly not going to start with this problem.
 
that's why I didn't understand your ''allowable words'' ... some combinations will be new words .. some will be existing words .. plus following the rules ... but I am not into math .. I don't know how to calculate that ... :rolleyes:
 
If you want anyone to be interested in helping you, at least tell us why in the world you would want to count with such a ridiculous set of conditions? You initially just said "I wonder", suggesting mere curiosity; then you said, "I need it".

Ultimately, as has been suggested, this is not a math problem; it is not at all interesting mathematically; and you express no interest in learning math, so it is not interesting pedagogically. I have no motivation at all to spend any time on this. So I'm out.
 
someone answered me partly in another forum ...

Let's start with simpler constraints. Let's say there are 5 vowels and 21 consonants and every word needs a vowel.

Then there are 5 one-letter words.

There are 21 x 5 = 105 two-letter words of the form CV, 105 of the form VC, and 25 of the form VV, total 235.
So there are 235 + 5 = 240 words of length <= 2.

For three-letter words, there are
5 x 5 x 5 = 125 of the form VVV
5 x 5 x 21 = 525 of each of the forms VVC, VCV, CVV, total 1575
5 x 21 x 21 = 2205 of each of the forms VCC, CVC, CCV, total 6615
total 8315 three-letter words
total 8555 words of length <= 3.

We could continue this for length 4 and above, but obviously the possibilities just in terms of C and V get more and more complicated as you go to bigger numbers - even without your extra constraints like "no more than . . . unless . . ." We would need a general formula for the number of combinations for each type (CVVV, CCVV, CVCV, etc.), and another formula for how to add them up, and yet another formula for how to add them to the totals for smaller numbers.

I've tried doing this before, for vaguely similar problems, but it's beyond me (a moderate mathematician) to come up with general formulae. I have an idea they involve things called Catalan numbers. Also I've had too much gin and tonic to go any further. (So, apologies if some of my numbers are slightly wrong.)

... how can I continue from here and use the proposed constraints?
 
Jivago said:
someone answered me partly in another forum ...
Let's start with simpler constraints. Let's say there are 5 vowels and 21 consonants and every word needs a vowel.
Then there are 5 one-letter words.
There are 21 x 5 = 105 two-letter words of the form CV, 105 of the form VC, and 25 of the form VV, total 235.
So there are 235 + 5 = 240 words of length <= 2.
For three-letter words, there are
5 x 5 x 5 = 125 of the form VVV
5 x 5 x 21 = 525 of each of the forms VVC, VCV, CVV, total 1575
5 x 21 x 21 = 2205 of each of the forms VCC, CVC, CCV, total 6615
total 8315 three-letter words
total 8555 words of length <= 3.
Click to expand...
Here is a much simpler way of computing those numbers: SEE THIS LINK.
If you need more than twelve just change \(N=1\text{ to whatever}\) hit enter.
 
THANK YOU pka ... in another forum that person who helped me continued today with this :

No, sorry, as I said, it's too much for me. If I needed to, I could possibly work out ways of getting some of the constraints in, but not all the ones you ask.

There's a simpler way of getting numbers with only that one constraint that there must be a vowel. A word of length n can have any of the 26 letters in the first place, any of them in the second, and so on, so there are 26n possibilities. But we want to exclude all those of type CCC..., nothing but consonants. There are 21 consonants so there are 21n possible all-C words.

For example, for n = 2 the total allowed is 262 − 212 = 676 − 441 = 235.
For n = 3 it is 263 − 213 = 17 576 − 9261 = 8315. (Luckily, those both match my other calculation above!)
For n = 4 it is 264 − 214 = 456 976 − 194 481 = 262 495, which would have been very difficult to do piece by piece.
For n = 5 it's 7 797 275, for n = 6 it's 223 149 655, which is getting absurdly large, and so on.

... is it correct right?
 
Jivago said:
No, sorry, as I said, it's too much for me. If I needed to, I could possibly work out ways of getting some of the constraints in, but not all the ones you ask. There's a simpler way of getting numbers with only that one constraint that there must be a vowel. A word of length n can have any of the 26 letters in the first place, any of them in the second, and so on, so there are 26n possibilities. But we want to exclude all those of type CCC..., nothing but consonants. There are 21 consonants so there are 21n possible all-C words.
For example, for n = 2 the total allowed is 262 − 212 = 676 − 441 = 235.
For n = 3 it is 263 − 213 = 17 576 − 9261 = 8315. (Luckily, those both match my other calculation above!)
For n = 4 it is 264 − 214 = 456 976 − 194 481 = 262 495, which would have been very difficult to do piece by piece.
For n = 5 it's 7 797 275, for n = 6 it's 223 149 655, which is getting absurdly large, and so on.
Click to expand...
Here is the table I generated. You can check the numbers. I can tell you that mine are correct.
The formula for strings of length\(N\) is \(26^N-21^N\) that is all possible strings of length \(N\) minus the number of strings of consonants .
twelve.gif

In this table each entry is the sum of all of length \(\le N\) i.e. \(\sum\limits_{k = 1}^N {\left[ {{{26}^k} - {{21}^k}} \right]} \)
 
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