# mcnuggets

mcnuggets, a MATLAB code which counts M(N), the number of ways a given number N of Chicken McNuggets can be assembled, given that they are only available in packages of 6, 9, and 20.

### Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

### Languages:

mcnuggets is available in a MATLAB version and an Octave version and a Python version.

### Related Programs:

change_diophantine, a MATLAB code which sets up a Diophantine equation to solve the change making problem, which counts the number of ways a given sum can be formed using coins of various denominations.

change_dynamic, a MATLAB code which uses dynamic programming to solve the change making problem, which counts the number of ways a given sum can be formed using coins of various denominations.

change_greedy, a MATLAB code which uses the greedy method to seek a solution to the change making problem, which tries to match a given amount by selecting coins of various denominations.

change_polynomial, a MATLAB code which uses a polynomial multiplication algorithm to count the ways of making various sums using a given number of coins.

combo, a MATLAB code which includes many combinatorial routines.

diophantine_nd, a MATLAB code which is given a Diophantine equation in N variables, and returns all strictly positive solutions, or all nonnegative solutions.

football_dynamic, a MATLAB code which uses dynamic programming to count the ways of achieving a given score in football.

knapsack_01_brute, a MATLAB code which uses brute force to solve small versions of the 0/1 knapsack problem;

knapsack_dynamic, a MATLAB code which uses dynamic programming to solve a knapsack problem.

knapsack_greedy, a MATLAB code which uses a greedy algorithm to estimate a solution of the knapsack problem;

mcnuggets_diophantine, a MATLAB code which uses Diophantine methods to find the ways a given number N of Chicken McNuggets can be assembled, given that they are only available in packages of 6, 9, and 20.

partition_brute, a MATLAB code which uses brute force to seek solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

partition_greedy, a MATLAB code which uses a greedy algorithm to seek a solution of the partition problem, in which a given set of integers is to be split into two groups whose sums are as close as possible.

satisfy_brute, a MATLAB code which uses brute force to find all assignments of values to a set of logical variables which make a complicated logical statement true.

subset, a MATLAB code which enumerates, generates, ranks and unranks combinatorial objects including combinations, partitions, subsets, index sets, and trees.

subset_sum, a MATLAB code which seeks solutions of the subset sum problem, in which it is desired to find a subset of a set of integers which has a given sum.

subset_sum_brute, a MATLAB code which uses brute force to solve the subset sum problem, to find a subset of a set of integers which has a given sum.

test_values, a MATLAB code which supplies test values of various mathematical functions, including Abramowitz, AGM, Airy, Bell, Bernoulli, Bessel, Beta, Binomial, Bivariate Normal, Catalan, Cauchy, Chebyshev, Chi Square, Clausen, Clebsch Gordan, Collatz, Cosine integral, Dawson, Debye, Dedekind, dilogarithm, Exponential integral, Elliptic, Error, Euler, Exponential integral, F probability, Fresnel, Frobenius, Gamma, Gegenbauer, Goodwin, Gudermannian, Harmonic, Hermite, Hypergeometric, inverse trigonometic, Jacobi, Julian Ephemeris Date, Kelvin, Laguerre, Laplace, Legendre, Lerch, Lobachevsky, Lobatto, Logarithmic integral, Log normal, McNugget numbers, Mertens, Mittag-Leffler, Moebius, Multinomial, Negative binomial, Nine J, Normal, Omega, Owen, Partition, Phi, Pi, Poisson, Polylogarithm, Polyomino, Prime, Psi, Rayleigh, Hyperbolic Sine integral, Sigma, Sine Power integral, Sine integral, Six J, Sphere area, Sphere volume, Spherical harmonic, Stirling, Stromgen, Struve, Student, Subfactorial, Student probability, Three J, Transport, Trigamma, Truncated normal, van der Corput, von Mises, Weibull, Wright omega, Zeta.

tsp_brute, a MATLAB code which is given a city-to-city distance map, and solves the traveling salesperson problem (TSP), using brute force.

tsp_descent, a MATLAB code which is given a city-to-city distance map, chooses an initial tour at random, and then tries a number of simple variations, seeking to quickly find a tour of lower cost.

tsp_greedy, a MATLAB code which is given a city-to-city distance map, picks a starting city, and then successively visits the nearest unvisited city.

tsp_random, a MATLAB code which is given a city-to-city distance map, and then randomly samples a number of possible tours, to quickly seek a tour of lower length.

### Reference:

1. Nick Berry,
Chicken Nugget Numbers,
https://datagenetics.com/blog/august22015/index.html
Posted 02 August 2015.
2. John D Cook,
The Chicken McNugget Monoid,
https://www.johndcook.com/blog/2022/10/10/mcnugget-monoid/
10 October 2022.

### Source Code

• mcnugget_number_values.m, returns some sample values of M(N), the number of ways of getting N Chicken McNuggets;
• mcnugget_ways.m, returns the number of ways of getting N Chicken McNuggets for 0 <= N <= NMAX;
• mcnugget_solvable.m, determines whether there is any solution of the McNuggets problem for a given number N.

Last revised on 24 December 2022.