# Tagged Questions

41 views

### Winning strategies in multidimensional tic-tac-toe

This question is a result of having too much free time years ago during military service. One of the many pastimes was playing tic-tac-toe in varying grid sizes and dimensions, and it lead me to a ...
57 views

### Sparsest matrix with full inverse

What is the sparsest matrix in $\mathbb R^{n,n}$ such that the inverse is full? I.e. I am looking for a matrix $A\in \mathbb R^{n,n}$ with as few non-zero entries as possible, such that $A^{-1}$ has ...
59 views

### Largest factor of sum of all 3-digit numbers…

What is the largest number (so, yes, I am looking for a discrete integer not an algebraic expression) by which the sum of all 3-digit numbers formed with the non-zero, distinct digits a, b, and c MUST ...
48 views

### How do you evaluate $a^b$ where b is irrational using only basic operators.

How would you evaluate $a^b$ where b is irrational and you can only use +,-, multiplication, division, and rational powers. For example $2^\pi.$ We know $2^2$ = $2\times2$ etc... but when the power ...
85 views

### Question About the Solutions to the Eight Queens Problem [closed]

How is $a_{15}n_8e_9k_5f_{10}d_7b_4m_6$ a solution to the Eight Queens problem? J. W. L. Glaisher, On the Problem of the Eight Queens, Philosophical Magazine, 1847 says that each one of these terms ...
348 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 ...
35 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 ...
43 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 ...
61 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 ...
81 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 ...
125 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 ...
45 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 ...
48 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) + ...
194 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 ...
112 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. ...
57 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 $[y_1*y_2*\dots y_n, y_2*\dots*y_{n}, \dots y_n]$ ...
53 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 ...
41 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 ...
133 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. } ...