Challenge #148: Rotating Century Puzzle

[JoeM]

This week, we got a real puzzler of a puzzle. Before we talk a bit about it, a big shout out and thanks to @patrick_digan, @brianaburke002, and @DultonM for sending me this challenge and solution. If anyone here every comes across a great challenge, feel free to message us with your idea! Some of our best challenges come from people like Patrick, Briana, and Dalton who come up against a problem and challenge themselves to solve it in Alteryx.

Let's try and solve this puzzle using Alteryx! There are 6 Rings  in this puzzle, with 6 numbers in each ring. Notice that you can rotate the rings and get 6 different rows of data. For example, one row could have 22 in Ring 1 (outermost), 7 in Ring 2, 16 in Ring 3,  2 in Ring 4, 18 in Ring 5 and 4 in Ring 6 (innermost). Summing these up, that row has a value of 22+7+16+2+18+4=69. The goal is to rotate the Rings until all 6 rows sum up to 100. For example, you could rotate it to get 15+12+13+26+5+29=100, but the next row would necessarily be 20+14+32+8+34+6=114. Can you rotate the Rings to the correct position? 

[JoBen]

Cheers! This was a lot of fun!

Spoiler

I used an iterative macro to simulate a turning of each circle. Here is what I came up with.

My WorkflowMy Iterative Macro

[jdunkerley79]

Fun one.

Spoiler

[CharlieS]

The idea of an iterative macro got stuck in my head when I started. I was finished by the time I realized how inefficient the solution was. Oh well, it works. 

[robertlenius]

Couldn't figure out at first how to automatically get the answer, instead built a macro to mimic the rotations so you can play the game as it was intended.

Spoiler

[sprodger]

My Solution (not the neatest) 

Spoiler

[JosephSerpis]

Challenge Completed 

[EW]

Mine is a bit of a trainwreck, but it seems to get the job done.  RIP, my brain!

Spoiler

[jasperlch]

Solution attached.

[estherb47]

Didn't finish early enough today for the first approach to be a unique solution, so added another :)

Spoiler

Create all combinations of wheels with Append Fields.

First approach was like many, using MOD to give each arrangement of the rings a unique code. Matching codes mean they're all in the same arrangement (you can add a summarize tool, and there are a total of 6 records per unique code). Check which spokes add up to 100. Count the total records in each unique code, and filter out for the code that appears 6 times in the result. Join back to the data to pull in the values and remove unwanted field.

Second approach, had to be different. Took a little longer. Instead of the matching unique codes, created a string that shows the position of each wheel (e.g., 112233), and then the position of the next set of numbers as you move clockwise (e.g. 223344). Filter out for spokes that add to 100, and join back to original data to bring in the next spoke clockwise for each of those arrangements - join on next position field on those that add to 100 to position field on original data. Filter out for spokes in the second match that add to 100. Still more than 6 records. Rinse and repeat join and filter process. Down to 6 records!! Check that the positions make sense

PosString	NextPosString
112231	223342
223342	334453
334453	445564
445564	556615
556615	661126
661126	112231

Reorder rows, and remove fields we don't need

FUN!!!!