Using Malcolm’s Switch puzzles, I am mentally backpropagating efficient choice paths to a solution. I use Malcolm’s Switch puzzles because his use of fixed C’s helps narrow choices. I don’t know if this will reduce efficacy of strategy creation.
Switch Puzzles are made up of a combination of single NT’s and independent NT threads.
Single NT ’s are in loops in each State.
NT threads cut across States and must always alternate between 1 or 2 choices given what an adjacent NT thread choice was.
The threaded nature of RNA switch puzzles is a key visualization that distinguishes them from single state RNA puzzles.
To resolve Switch puzzle, it is helpful to:
1. identify each thread
2. know the structure characteristics of each NT in the thread
Being able to holistically look at an entire thread and the structure characteristics of each NT in that thread across all Switch States makes selection much easier. To do this, imagine matrixes containing this information - see below.
Note: when I talk about energy differential, I mean the difference between the sum of energies in all three States in the the Target Mode versus Natural Mode.
First, a vector table that lists each important structural characteristic, then includes the NT# if the NT has that characteristic in that State. So for example in below, the table indicates that NT3 is in a 1-1 Loop in State 2.
“Boosts” indicate that the NT position in that State is in a boosting spot.
“Stem ends” - the NT is at a stem end (with stem > 2 pairs)
“1,2 NT stems” - the NT is in either a 1 or 2 pair stem
Secondly, create Matrixes for both Single NT’s and Threads that show their characteristics.
The NT Loop Matrix below shows every NT that is a loop in all 3 States, the actual answer, what the matrix rules suggest and if that NT is in either a boost position (B) or a 1-1 Loop (1L).
Here are the Loop Matrix Rules I currently use:
1. If boosts within loop have already been exhausted, use A (you have to visually see this)
2. If NT has 2 or 3 boost potentials, including 1-1L, use G
3. If NT is in only one 1-1 Loop, use A but retain G as a high probable choice
The Thread Matrix lists all NT threads and then shows if they are fixed C’s, the answer, what the model suggests and then whether they are in a boost or 1-1 Loop, or at a stem end (“E” for 1 or 2 stems and “e” for stems > 2NT’s.
The Thread Matrix below shows the 2 longest threads in Puzzle 423. For Thread #1, all the choices are fixed because the thread contains so many fixed C’s.
NT’s highlighted in blue indicate that they also branch off to the next NT highlighted in blue.
NT’s highlighted in yellow indicate they both branch off from the NT just above them.
NT’s choices highlighted in red indicate that the model made an incorrect selection.
The rules I am using for selecting NT’s in threads are:
First follow any required choices from fixed C’s (including using U’s after G’s because in these puzzles Malcolm says no more C’s are needed).
Then if any NT in is a 1-1 Loop and is any boost position, use a G rather than an A if that is appropriate sequentially.
Also use G if there is at least a combination of 3 boosts or stem ends if appropriate sequentially.
Otherwise use A’s or U’s.
Using the method described above with the Steps below, I solved Puzzle #423. I selected puzzle #423 because no one else had solved it and it has been out there awhile. I will continue within universe of Malcolm’s switch puzzles to test and develop rule sets and see what kinds of pattern problems remain unresolved.
Step 1. Complete NT Loops using NT Loop Matrix and rules
Step 2. For Threads containing fixed C’s, complete threads, going from longest to shortest, using Thread Matrix and rules
Step 3. For remaining threads, going from longest to shortest, use AU selections that minimizes energy differential (use G’s where thread matrix rules indicate)
Step 4. In areas where State is in red, try G’s in any remaining 1-1 Loops or boosts and use if it lowers energy differential.
Step 5. Altering single pair threads and use if lowers energy differential.
Step 6. In areas of red, try replacing A’s with G’s (often to repel undesired linkages) - and use if it lowers energy differential.