# strings

1. ### Fibonacci Seq bit string proof. Show that pattern can't have three consecutive 1s

I'm having a little trouble figuring out how to prove this. So, the sequence is as follows: S0 = 0 S1 = 1 S(n-2)S(n-1) for all n >= 2 That means S2 = 10 S3 = 101 S4 = 10110 S5 = 10110101 Now the question that I'm stuck on is: Prove that the pattern can't have three consecutive ones...
2. ### Finding a recurrence formula for strings of numbers, thanks

Hi guys, I am stuck on the logic of this problem so any hints in the right direction would be greatly appreciated. Given the set a_n of sequences with length n composed with the elements (1 to 5), 5 elements, I need to find a recurrence formula for the number of sequences that would not...
3. ### rotating strings of vectors

Let's say I have a vector, (3.8, 0), and I add a vector to it that I know will give me a resulting vector of equal magnitude (-1.11, 2.69). By doing this I have effectively rotated the original vector by a certain amount. My question is, utilizing only this first vector and the added vector...
4. ### How many bit strings?

How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1?
5. ### Strings of eight English letters

How many strings of eight English letters are there that contain exactly one vowel, if letters can be repeated? My attempt: Let us first find the number of strings that contain at least one 'a' and no other vowels. Total number of strings including 'a' but excluding the other vowels $=22^8$...
6. ### Strings of three decimal digits

How many strings of three decimal digits have exactly two digits that are 4s? Solution: 44x - 9 strings 4x4 - 9 strings x44 - 9 strings Total: 27 strings I get that. But what is wrong with this line of reasoning? I have two 4s with me. I have 3 positions for the first one and 2 for the...
7. ### Strings broken in Java

Ashes 2015 Live Stream British Open 2015 Live Stream Ashes 2015 Live Stream
8. ### Strings

I don't really get the question that is being asked. Let S be the set of binary strings of length 30 with 10 1’s and 20 0’s. Let Abe the set of the first 30 positive integers (A := [30] = {1, 2, 3, . . . , 30}). Let B be the set ofall subsets of A containing 10 numbers. Find a bijection between...
9. ### Designing an algorithm with a finite amount of storage that accepts strings in L?

Hello everyone! :D First off, I'm not sure if this should go under Discrete Math, Number Theory, etc., so sorry if it's in the wrong spot! I am wondering how to create an algorithm WITHOUT using an unbounded amount of storage that can accept strings from L: Question: Let L be a language over...
10. ### Find a String of Minimum Length Not in the Language

In each case below, find a string of minimum length in {a,b}* not in the language corresponding to the given regular expression. a. b*(ab)*a* b. (a* + b*)(a* + b*)(a* + b*) c. a*(baa*)*b* d. b*(a + ba)*b*...
11. ### Repeats and strings

Ok so i don't know how to prove the following: Let S be a string and |S| its length. Let [i..j] be an interval such that 0 < i <= |S| and 0 < j <= |S|. You can also refer to [i..j] as a substring of S. Let [i..j] be a maximum repeat such that [i..j] is repeated and [i..j+1] and [i-1..j] are...
12. ### Maximum Number of bit Strings

What is the maximum number of diﬀerent bit strings of length 8 you can have without having at least 2 bit strings that start with 0000 (four 0’s)?
13. ### Recurrence equations

Hi. Could you help me solve these equations? I know how to solve recurrence equations with only a_k[\tex] and scalars in, and sometimes I can also guess the formula and then prove it by induction. But I have no idea how to go about solving these: 1) a_{n}= \frac{ a_{n-1} ^{3} }{ a_{n-2}...
14. ### Determine a justification for how many different bit strings of length ten...

Determine an appropriate justification for how many different bit strings of length ten: i) remain unchanged if it is reversed, ie first bit is like the last one, then the first one and the second last and so on., as is the case for example the strings 1011001101 and 0101111010. ii) contains...
15. ### Relation of eight bit strings

Let R be the relation defined on the set of eight-bits strings by s1RS2 provided that s1 and s2 have the same number of zeros. (a) Show that r is an equivalent relation. (b) How many equivalence classes are there? (c) List one member of each equivalence class.
16. ### Prove there exists two strings

Let s1, s2, ..., s101 be 101 bit strings of length at most 9. Prove that there exist two strings, si and sj, where i not equal to j, that contain the same number of 0s and the same number of 1s. (eg: strings 001001 and 101000 contain the same number of 0s and the same number of 1s)
17. ### How many bit strings of length 12...?

contain at most ten 1's and at most four 0's? Im so lost :P Thanks!
18. ### Strings of letters with exclusion

Say you had the String "RRYYYZZZZ". The number of distinct combinations you could arrange these is: \frac{9!}{2!3!4!} What if we didn't allow any Y to touch an R. I"m at a loss at how to go about excluding those.
19. ### Proving strings generated by a grammar can be decomposed in a certain way

If I have a grammar S -> aSbS|epsilon With the language it generates represented by L and I want to prove that for all strings w = L - {epsilon}, w can be decomposed to w = a u b v where u and v exist in L, does the following proof make sense? If w has the same number of a's and b's, then...
20. ### Physics: Ball of Strings

This is less a question of physics and more one of the mathematical minutes, so please bear with me if this is a really dumb question. I am trying to understand an example equation in the textbook that went from [4(2m)^2] / [(4 * 10^-3m)^2] = 2 * 10^6m. It doesn't bother to explain the stages...