## Puzzle Archive

Tangled!

While on vacation in Terniquaternaria, Decimus got to experience the country’s traditional folkloric dance, which they call the “Yawn-ock“. The people of Terniquaternaria pride themselves on being rational, so they dance the Yawn-ock by the following strict rules. Four dancers hold one end of two long pieces of rope and never let go. They initially take the following positions:

A                     D
\_________/
__________
/                    \
B                     C

During the entire dance, only two types of move are allowed:

• The entire group rotates 90 degrees counterclockwise (ie the dancer in A moves to B, dancer in B moves to C, etc). This step is called a “Rotate” (R).
• Dancers in C and D swap places, with D holding the rope up while C is passing under. This step is called a “Swap” (S).

From the initial configuration, a dance master calls out successive R/S steps randomly, that the dancers diligently execute accompanied by music. After this, there is usually quite a tangled mess of rope in the middle!

A participant from the crowd can then step forward and attempt to untangle the ropes by shouting a sequence of the same two moves as above, that the dancers execute. If this person succeeds in fully untangling the ropes, he/she gets crowned King/Queen for the day!

Decimus took careful note of the sequence of moves executed by the dancers:

He would really like to become King, no matter how much research it might take. What sequence would untangle the ropes?

2020-09-09 update: Turns out the Yawn-ock dancers have a limited amount of endurance, and prefer a shorter sequence of untangling commands over a longer one. As such we will keep the top of our leaderboard of solvers ranked by number of commands in the solution, with the solver with the shortest correct solution at the top. Any solvers that have already submitted can re-submit if they’d like to record their most efficient untying maneuver!