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Backgammon #2 - Your turn!
A previous problem in this occasional series (Problem 45967) set up a possible representation of a backgammon board: White ston...
23 hours 前
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Backgammon #1 - Pip Count
The following is a possible representation of a backgammon board: White stones are represented by positive integers Red stones ...
23 hours 前
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Newton Interpolation
Given a set of measurements of dependent variables in a vector, Y, that vary with one independent variable in a vector, X, calcu...
23 hours 前
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Augmented Lagrange Multiplier (ALM) Method
Write a function to find the values of a design variable vector, _x_, that minimizes a scalar objective function, _f_ ( _x_ ), g...
23 hours 前
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Spin Matrices
The spin of a particle is a fundamental property in quantum physics. We shall inspect below matrix representations of such spin ...
2 days 前
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Hungry Snake
Who hasn't played <http://en.wikipedia.org/wiki/Snake_%28video_game%29 the Snake game> when they were little? It's quite hard ...
2 days 前
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Calculate integrals using numerical methods 3.
Now let's compare the 2 previous rules. Using the "Simpson 1/3" rule and the trapezoidal rule, NOT THE SIMPLE ONES, calculate th...
2 days 前
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Calculate integrals using numerical methods 2.
Calculate the following integral(I) using the SIMPLE(thus n =1) trapezoidal rule: The llimits(a,b) of the integral will be gi...
2 days 前
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Calculate integrals using numerical methods 1.
Calculate the following intergral using the SIMPLE "Simpson 1/3" rule: Further explanation: a is the upper limit of the inte...
2 days 前
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Nash Equilibrium
In game theory, a player's *strategy* is any of the options that can be chosen in a setting where the pay-off depends not only o...
3 days 前
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Let's Make A Deal: Criminal Minds
The game of Let's Make A Deal proceeds as follows; The player is given the choice of three doors: Behind one door is a car; b...
3 days 前
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Let's Make A Deal: The Player's Dilemma 2
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. Y...
3 days 前
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Let's Make A Deal: The Player's Dilemma
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. Y...
3 days 前
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God of War: The Chains Of Olympus
The Spartan warrior, Kratos, is held by a chain of _n > 1_ links in the underworld. His only chance of survival is to break the ...
3 days 前
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The Generalized-N Eggs Problem
A firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building with...
3 days 前
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Response of First Order Control Systems
In practice, the input signal to an automatic control system is not known ahead of time but usually random in nature. Thus, in t...
3 days 前
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Nodal Voltage of Resistor Ladder Network
* You have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltme...
3 days 前
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Implement Shor's algorithm
Shor's algorithm, proposed in 1994 by Peter Shor, is an algorithm for factoring numbers that runs in polynomial time (polynomial...
3 days 前
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Array size along k-th dimension
Given an n-dimensional array M, find the size of M along the k-th dimension (1 <= k <= n), without using size(), height() or wid...
3 days 前
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Solve the matrix equation AXB + X + C = 0 for X
Let A, B, and C be square matrices of equal size, and let the matrix X be defined by the matrix equation A * X * B + X + ...
3 days 前
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Optimal saving in Solow's classical growth model
Let us consider a simplified version of Solow's classical growth model. Let , , , and denote production, the capital stock, l...
3 days 前
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Compute rational expectations in a static, linear NKM model
Consider a static, linear approximation of the baseline New Keynesian macroeconomic model. This can be described by an IS equati...
3 days 前
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Calculate the volume of the intersection of two balls
Consider two balls (solid spheres) in , with radius and respectively. Suppose that the distance between the centers of the two...
3 days 前
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Create an empty array
Suppose you need an empty array. e = [] will give you one, but it's a double array, which may not help if you need a differen...
3 days 前
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Remove runs of at least n consecutive NaNs
This problem is inspired by Dyuman Joshi's problem 58329. Given a row vector x and a natural number n, remove all runs of at lea...
3 days 前
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Swap the column given with another one!
We have a random sized matrix A. You have to change the nth column with the kth column. The result must be a matrix B. For exam...
3 days 前
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Find circular arc length, sector area and segment area
Given a circular arc passing through the points P = [ x1 y1 ] and Q = [ x2 y2 ] such that the center angle of the arc (in degree...
4 days 前
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Rotate matrix 60 degrees
Given a 2*m-1 by 4*m-3 matrix in which certain elements form a hexagon of side length m, rotate the hexagon 60 degrees countercl...
4 days 前
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Mystery problem
Given integer x between 1 and 50, return integer y=mystery(x), where mystery(1) = 111 mystery(6) = 809 ... mystery...
4 days 前
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Convert vector of strings to lower triangular matrix
Given a non-empty vector vec of strings, please put its elements into the lower triangular half of a square matrix M column-wise...
5 days 前
