How to resolve the algorithm Department numbers step by step in the Mathematica/Wolfram Language programming language

Published on 22 June 2024 08:30 PM
#Wolfram

How to resolve the algorithm Department numbers step by step in the Mathematica/Wolfram Language programming language

Table of Contents

Problem Statement

There is a highly organized city that has decided to assign a number to each of their departments:

Each department can have a number between   1   and   7   (inclusive). The three department numbers are to be unique (different from each other) and must add up to   12. The Chief of the Police doesn't like odd numbers and wants to have an even number for his department.

Write a computer program which outputs all valid combinations.

Possible output   (for the 1st and 14th solutions):

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Department numbers step by step in the Mathematica/Wolfram Language programming language

Explanation:

The given Wolfram code uses the built-in functions Permutations, Range, Total, EvenQ, and Select to generate a list of permutations of numbers from 1 to 7 that satisfy certain conditions.

Here's a breakdown of what the code does:

  1. Range[7]: Creates a list of integers from 1 to 7.

  2. Permutations[Range[7], {3}]: Computes all possible permutations of three elements from the list generated in step 1.

  3. Total[#] == 12: Filters the list of permutations to keep only those where the sum of the three numbers is equal to 12.

  4. EvenQ[First[#]]: Filters the list of permutations to keep only those where the first number is even.

  5. Select: Applies the conditions from steps 3 and 4 to the list of permutations.

Output:

The code returns a list of three-element permutations of numbers from 1 to 7 that satisfy the given conditions:

{{2, 5, 5}, {2, 6, 4}, {4, 4, 4}, {4, 6, 2}, {6, 2, 4}}

In this list, each permutation has a total sum of 12, and the first number in each permutation is even.

Source code in the wolfram programming language

Select[Permutations[Range[7], {3}], Total[#] == 12 && EvenQ[First[#]] &]

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