1
vote
1answer
24 views

raBinomial distribution with dependent trials?

I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, ...
14
votes
2answers
297 views

Does every “balloon” (dragon, tadpole, canoe paddle) admit a graceful labeling?

8/18/14 Edit: If anyone has a copy of a related reference, then I would be happy to see it. For now, I am accepting the answer below and considering the question answered in the affirmative: Yes. ...
1
vote
2answers
89 views

How can I solve this problem without having to do it by hand?

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
0
votes
1answer
72 views

How can I solve this problem without doing it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
1
vote
2answers
71 views

Is there any way to solve this problem without having to do it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement. Is there any way to group ...
1
vote
2answers
25 views

Finding the number of solutions satisfying an equation?

Given one condition $x_1+x_2+x_3=n$ where n is known number. Given a set of data X={$a_1,a_2....a_n$}. Can you help me find all possible cases satisfying the above condition $x_1+x_2+x_3=n$ ???
4
votes
1answer
79 views

Can someone please clarify combinations vs permutations?

I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way. There are basically infinite scenarios ...
2
votes
2answers
78 views

Find $\max_{\sigma \in S_n}\sum_{i=1}^n|\sigma(i)-i|$ where $S_n$ is the group of permutations on $n$ letters (Greedy algorithm shows up?)

Find $\max_{\sigma \in S_n}\sum_{i=1}^n|\sigma(i)-i|$, where $S_n$ is the symmetric group of permutations of $n$ symbols. So, the story goes like this: When I first saw the problem, I thought the ...
0
votes
1answer
46 views

conditional probability Pc(B)

I am looking for the probability of Pc(B) where the event of B={no two people are born in the same month} and event C= {exactly three people were born in the summer of june, july august} and there are ...
0
votes
1answer
58 views

Pigeonhole Principle to solve question straightforward

A store wants to celebrate its anniversary and will give a $200 shopping certi cate to the first customer to enter the store whose birthday is the same as that of two other previously admitted ...
3
votes
3answers
420 views

Fractions in Ancient Egypt

In ancient Egypt, fractions were written as sums of fractions with numerator 1. For instance,$ \frac{3}{5}=\frac{1}{2}+\frac{1}{10}$. Consider the following algorithm for writing a fraction ...
4
votes
1answer
170 views

Board $7\times 7$ problem

An aid in this problem: On a board of $7 \times 7$ each box is painted red or blue so that any square on the board has at least two neighboring boxes blue. determine as little blue boxes that can be ...
1
vote
2answers
56 views

Show that one person must have x amount of dollars

A group of six friends discover they have a total of \$21.61 with them on a trip to the movies. Show that one or more of them must have at least \$3.61. How should I approach this problem? I can see ...
3
votes
0answers
135 views

Difference between two sets of data points

I'm making a simple calibration of a z-stage, by measuring a number of points in one direction with a constant $\Delta$Z between each sample. Then I reverse the direction and measure the same number ...
5
votes
3answers
107 views

Closed formula for linear binomial identity

I have the following identity: \begin{equation} m^4 = Z{m\choose 4}+Y{m\choose 3}+X{m\choose 2}+W{m\choose 1} \end{equation} I solved for the values and learned of the interpretation of W, X, Y, and ...
0
votes
0answers
59 views

Define a problem using chernoff bounds

We are preparing this for an exam. Given the division of a plane into a number of regions of different sizes. We would like to find, or guess, which is the biggest region, by doing the following. We ...
0
votes
1answer
834 views

Can this crate have even numbers in all rows and columns?

A milk crate holds 24 bottles in four rows and six columns. Can you put 18 bottles of milk in the crate so that each row and each column of the crate have an even number of bottles in it?