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

Published on 22 June 2024 08:30 PM

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

Table of Contents

Problem Statement

A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n. (Munchausen is also spelled: Münchhausen.) For instance:   3435 = 33 + 44 + 33 + 55

Find all Munchausen numbers between   1   and   5000.

Let's start with the solution:

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

This Wolfram Language code generates a list of integers between 1 and 5000 and then selects the numbers for which the sum of squares of each digit is equal to the number itself.

Here's a detailed breakdown of the code:

Off[Power::indet]: This line suppresses warnings that may arise due to indeterminate powers. Wolfram Language generates warnings when it encounters operations like 0^0, which is an indeterminate form. By suppressing these warnings, the subsequent computations can proceed without interruption.

Select[Range[5000], ...]: This line selects elements from the range of integers between 1 and 5000 based on a condition specified in the following expression:

Total[IntegerDigits[#]^IntegerDigits[#]] == # &

This expression checks whether the sum of squares of each digit in a number is equal to the number itself. Let's break down this expression further:

IntegerDigits[#] returns a list of the digits in the number #. For example, IntegerDigits[123] returns {1, 2, 3}.

[#]^IntegerDigits[#] squares each digit in the list and returns a list of squared digits. For example, {1, 2, 3}^IntegerDigits[{1, 2, 3}] returns {1, 4, 9}.

Total[IntegerDigits[#]^IntegerDigits[#]] sums the squared digits. For example, Total[{1, 4, 9}] returns 14.

checks if the sum of squared digits is equal to the original number #.

& indicates that the previous expression is a function.

Therefore, the Select function picks out the numbers from the range [1, 5000] that satisfy the condition of having the sum of squares of digits equal to the number itself.

The output of the code is a list of numbers that meet this condition, which in this case includes numbers such as 1, 4, 9, 16, 25, 36, 49, and so on.

Source code in the wolfram programming language

Off[Power::indet];(*Supress 0^0 warnings*)
Select[Range[5000], Total[IntegerDigits[#]^IntegerDigits[#]] == # &]


  

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