# Tagged Questions

Questions on optimization constrained to integer variables.

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### Determining information in minimum trials (combinatorics problem)

A student has to pass a exam, with $k2^{k-1}$ questions to be answered by yes or no, on a subject he knows nothing about. The student is allowed to pass mock exams who have the same questions as the ...
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### Good software for linear/integer programming

I never did any linear/integer programming so I am wondering the following two things What are some efficient free linear programming solvers? What are some efficient commercial linear programming ...
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### Are there ways to solve equations with multiple variables?

I am not at a high level in math, so I have a simple question a simple Google search cannot answer, and the other Stack Exchange questions does not either. I thought about this question after reading ...
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### Mean and Median in a Classic River Crossing Problem

Consider the following classic problem: Four people on the west side of a river wish to use their single boat to get to the east side of a river. Each boat ride can hold at most two people, and the ...
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### Integer programming feasibility is NP-what

What is the complexity class of the general problem of integer programming feasibility? The sources I've looked at are, in my opinion, very confusing. Some say NP-hard, some say NP-complete. Some do ...
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### solve $54 x + 16 y = 2400$ for integer values of x,y

How to get integer values for x and y that satisfy: $$54 x + 16 y = 2400$$ Someone told me that I can do it using Euclid-Wallis algorithm, but I don't understand it so, if there isn't any else ...
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### Linear constraints to placing N queens on an N x N chessboard?

I'm trying to formulate the problem of placing N queens on an N x N chessboard such that no two queens share any row, column, or diagonal. I managed to define my decision variable as x[n][n], a ...
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### Maximizing the number of non-crossing lines between a number of points

Suppose I have a number of points in 2-dimensional space. I want to draw as many lines between the points as possible such that no two lines cross. Hoping for a polynomial time algorithm, I ...
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### Prove or disprove a chessboard with diagonal corners removed, cannot be tiled with L shape pieces or size 2

I think this is impossible, but I don't know how to prove an integer solution doesn't exist for a given equation. Here's my approach: First, observations: The removed tile will be of the same color. ...
Is there a way to find all integer solutions to a hyperbola equation? If it helps, I am specifically looking at "square" hyperbolas (i.e. of the form $\frac{x^2}{z} - \frac{y^2}{z}=1$), where z is an ...