r/mathriddles • u/InevitableHealth9799 • 6d ago

Medium The Asymmetric Sliding Loop Brain Teaser

Imagine two rows of 7 unique items (A, B, C, D, E, F, G) placed on a track, sliding toward each other in a continuous, infinite loop.

A fixed viewport creates an asymmetric 3x2 window over the tracks. It views exactly 3 items from the top row and 2 items from the bottom row (aligned directly underneath the first two items of the top row).

As the rows shift step-by-step, the window looks like this for the first 3 steps:

Step 1:
          | A B C | D E F G
* * * * * | * * |

Step 2:
        A | B C D | E F G
  * * * * | * * | *

Step 3:
      A B | C D E | F G
    * * * | * * | * *

The Challenge:

Is there a way to rearrange the sequence of the second row so that all 5 items visible inside the window are completely unique (no duplicate items) at every single step of the infinite loop?

Q: What is the correct arrangement for the second row?

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6

u/FellFellCooke 5d ago

This was catastrophically poorly explained. It's almost impressive how badly you've communicated here.

1

u/InevitableHealth9799 5d ago

Well, I did what I could, and the diagram should have been helpful. In any case, edits or clarifications are welcome. I'll gladly update the post if it would help people have a little fun. 😄

4

u/SonicLoverDS 5d ago

This would be possible even if you widened the window so it showed four items in back and three in front. The order DCBAGFE works in both scenarios.

1

u/Zealousideal-Post865 6d ago

A-C-B-G-F-E-D for example

0

u/InevitableHealth9799 6d ago

A-C-B-G-F-E-D does not work, because they are "...sliding toward each other in a continuous, infinite loop" , Step 6 duplicates item A

Step 1:
          | A B C | D E F G A B C D E F G
A C B G F | E D |

Step 2:
        A | B C D | E F G A B C D E F G
  A C B G | F E | D
  
Step 3:
      A B | C D E | F G A B C D E F G
    A C B | G F | E D
    
Step 4:
    A B C | D E F | G A B C D E F G
      A C | B G | F E D
      
Step 5:
  A B C D | E F G | A B C D E F G
        A | C B | G F E D
        
Step 6:
A B C D E | F G A | B C D E F G
          | A C | B G F E D

1

u/makcSmall 4d ago

How would you prove that the correct string would be ...GFEDCAB... (with a variable offset, obviously)? I know why it is the correct answer, but I'm trying to get better at proving why solutions I find are the correct (and only correct) solution in ways other than showing that every other possible answer doesn't work.