Challenge #475: The Collatz Conjecture

[AYXAcademy]

 

Hi Community members,

A solution to last week’s challenge can be found here. 

This challenge for the mathematicians at heart was submitted by Ippei Nakagawa (@gawa). Thank you, Ippei, for this challenge!

The Collatz conjecture, also known as the 3n + 1 problem, is a conjecture in mathematics named after Lothar Collatz, who introduced it in 1937. It is an unsolved problem in mathematics that is simple to state but difficult to prove. The problem is defined as follows:

1. Start with any positive integer N.
2. Apply the following rules:
   • If N is even, divide it by 2.
   • If N is odd, multiply it by 3 and add 1.
3. Repeat the process with the resulting number as much as necessary to reach the number 1. The conjecture states that no matter what positive integer N you start with, you will always eventually reach the number 1.

Here is an example:

Start with N=6:

• 6 is even, so 6/2=3
• 3 is odd, so 3×3+1=10
• 10 is even, so 10/2=5
• 5 is odd, so 5×3+1=16
• 16 is even, so 16/2=8
• 8 is even, so 8/2=4
• 4 is even, so 4/2=2
• 2 is even, so 2/2=1

A total of 8 steps were required in this example.

For this challenge, you need to create an iterative macro that simulates the repeated steps until reaching 1 for each number. Once the macro is created, your tasks are to:

• Generate the numbers from 1 to 10,000.
• Use the iterative macro to apply the Collatz conjecture to each number.
• Identify the maximum number of steps used to reach the number 1.

Need a refresher? Review the following lessons in Academy to gear up:

• Introduction to Macros in Designer
• Types of Macros in Designer
• Creating an Iterative Macro

Good luck!

The Academy Team

Download Start File

Download Solution File

[RWvanLeeuwen]

Here's my take

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iterative macro that starts with these three fields (manipulating the [Value] and incrementing the [Step])

[Pilsner]

I always enjoy the mathematical challenges!

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Macro:

 

[lwolfie]

Fun Monday Morning Challenge.

[RolandSchubert]

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[RWvanLeeuwen]

Quick tip for this challenge: I'd suggest keeping the number of iterations below 500.

I just tried generating 1,000,000 records and allowed for 1,000,000 iterations, but the last 432 records were not quite ready to be tackled using this routine. The last row that exited the program took less than 500 steps

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[AkimasaKajitani]

My solution. 

I don't use the macro.

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[mmontgomery]

C475

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Nice I-macro to start the week!

[TurboToad]

Fun Challenge! I added in a record ID to track which number had the most steps.

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[olga_strubbe]

I loved this challenge, thank you so much!  It was fun to build an iterative macro for this mathematical conjecture, in fact. 

My workflow and macro are included. 

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