3
votes
1answer
261 views

How can I use math to fill out my NCAA tournament bracket?

With the NCAA basketball tournament right around the corner and the conference tournaments just beginning, it's the perfect time to consider strategies to fill out an NCAA tournament bracket. How can ...
1
vote
1answer
31 views

matrix row/col mapping

Many square matrices are symmetric. i.e. $a_{i,j}=a_{j,i}$ For such matrices, we can only store the upper triangle elements, i.e. any $a_{i,j}$ for which $i<=j$. Assume a 10x10 matrix. Using this ...
0
votes
0answers
40 views

Waiting Time For Computer Cluster

There are $n$ computers. Computer users stay on their computers for a certain amount of time, $t$, throughout the day. Computer users come and go. How long will I have to wait, min/max, for a computer ...
0
votes
1answer
59 views

Scaling a cup to have a certain filling volume

I created a cup in Autodesk Inventor using lathe/rotation, ie I defined the profile and rotated it around an axis. I measured it's volume. By using Patch and Sculpt I filled the inner volume(which ...
0
votes
2answers
51 views

Solve for the angle of two straight lines on a 3 dimensional plane.

On a $3$ dimensional plane: Given that two vectors $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ are known and that each of these vectors belong to two separate straight lines ...
4
votes
1answer
119 views

Linear Algebra in curved space

We know that Euclidean geometry and Newtonian Physics are special cases that only work in a flat space-time. Got to thinking about linear algebra and matrices. Is linear-algebra a special subset of ...
-3
votes
1answer
42 views

Computation of integral [closed]

I want to compute this integral: \begin{equation*} J=\int_{0}^{1}\ln(p)\ln(1-p)p^{2}dp \end{equation*} It will be great if you can detail the proof. I tryed to do change of variable it does not ...
0
votes
0answers
45 views

Alternative more challenging problems to a simple supplementary/complementary problem

Original Question Find the measure of an angle if 80 degrees less than 3 times its supplement is 70 degrees more than 3 times its complement. The solution is simple. 3(180 - a) - 80 = 3(90 - a) + ...
0
votes
3answers
193 views

Finding values for $x$ and $y$ given ONE equation

Ok so I'm in precalculus right now and the directions on my homework seem to make no sense to me. I'm asked to find values for $x$ and $y$ given this equation: $y=x^{1/3}$ Doesn't this mean I could ...
1
vote
3answers
103 views

Rating changes and probability calculations for chess world championship

I have some interesting questions that have to do with the rating changes and calculations for the Anand-Carlsen world championship. Most of this has to do with solving a system of linear equations. ...
1
vote
0answers
56 views

Linear algebra function that creates decreasing product vector of original vector

For vector $y=[y_1,y_2,\dots y_n]$ , let $\gamma = \sum_{i=1}^n \gamma_i$ , and $\gamma_i(n-i+1)=y_n*y_{n-1}*\dots y_i$ so that $\gamma$ looks like $[y_1*y_2*\dots y_n, y_2*\dots*y_{n}, \dots y_n]$ ...
0
votes
1answer
52 views

Derive a formula to solve a specific task

I have a specific problem. I have 8 different variables a, b, c, d, e, f, g, h. Each of these variables has a score out of 5, where 1 is bad and 5 is good. So a max score of 45 and a min of 0. Of ...
0
votes
1answer
40 views

Adjust a range of given values. [duplicate]

If I have a number anywhere on the range 140 - 350 and I want to match it to the correlated range "0 - 360" what function can I run it through? i.e.:140 would go through the function and return 0.350 ...
1
vote
1answer
124 views

Linear Algebra Recreational Problem

For each positive integer $k$, find the smallest number $n_k$ for which there exist real $n_k$ by $ n_k$ matrices $A_1; A_2; ....; A_k$ such that all of the following conditions hold: $$ \text{ 1. } ...
6
votes
2answers
260 views

Vector spaces inquiry

Denote By $V$ the real vector spaces of all real polynomials in one variable, and let $P : V \rightarrow \mathbb{R}$ be a linear map. Suppose that $\forall$ $f,g \in V$ with $P(fg) = 0$ we have $P(f) ...
0
votes
1answer
621 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?
19
votes
1answer
397 views

Extracting individual race results from Mario Kart final scores

In Mario Kart, one "cup" involves 4 races, and after every race each racer gets points awarded based on what place they came in (better rank means more points). After playing it enough I grew curious ...
6
votes
1answer
419 views

Solving $n$-queens with determinants

I keep reading about a proposed method of finding solutions to the $n$-queens problem using determinants, but I can't find any specific details anywhere. Can somebody explain to me how to find ...
14
votes
2answers
849 views

any pattern here ? (revised 2)

for any positive number $k$, I have a $(k+1)*(k+1)$ matrix. I wonder if these matrices follow any "obvious" pattern. My goal is to guess the elements for matrix with $k=5$ and above (most probably in ...
11
votes
3answers
2k views

Lights out game on hexagonal grid

I greatly enjoyed the Lights Out game described here (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page). Its mathematical analysis is here (it's just ...