Step by Step solution about How to resolve the algorithm State name puzzle step by step in the Mathematica/Wolfram Language programming language

This Wolfram program generates and selects permutations of 4-letter subsets of U.S. state names, prioritizing those with the same first and last pair of letters. Let's break down the code step by step:

letters[words_,n_] := Sort[Flatten[Characters /@ Take[words,n]]]

This function takes two inputs: a list of words (or strings) and an integer n. It extracts the first n characters from each word in the list, flattens them into a single list, and sorts the resulting list. The purpose of this function is to compare the first and last characters of different permutations.

groupSameQ[g1_, g2_] := Sort /@ Partition[g1, 2] === Sort /@ Partition[g2, 2]

This function takes two input lists (or groups) and compares them. It partitions both groups into pairs of elements, sorts each pair, and then compares the sorted pairs from both groups. If the sorted pairs are equal, the function returns True, indicating that the groups have the same first and last pair of elements.

permutations[{a_, b_, c_, d_}] = Union[Permutations[{a, b, c, d}], SameTest -> groupSameQ]

This function takes a list of four elements and generates permutations of those elements. It uses the Union function to remove duplicate permutations and applies the SameTest option to use the groupSameQ function for comparison. This means that permutations with the same first and last pair of elements are considered duplicates and are discarded.

Select[Flatten[permutations /@ 
  Subsets[Union[ToLowerCase/@{"Alabama", "Alaska", "Arizona", "Arkansas", "California", "Colorado", "Connecticut", "Delaware", "Florida", 
     "Georgia", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine", "Maryland", 
     "Massachusetts", "Michigan", "Minnesota", "Mississippi", "Missouri", "Montana", "Nebraska", "Nevada", "New Hampshire", 
     "New Jersey", "New Mexico", "New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma", "Oregon", "Pennsylvania", 
     "Rhode Island", "South Carolina", "South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia", "Washington", 
     "West Virginia", "Wisconsin", "Wyoming"}], {4}], 1], 
letters[#, 2] === letters[#, -2] &]

In this part of the code, the program generates all possible 4-element subsets of the 50 U.S. state names in lowercase. It then creates permutations of each subset using the permutations function. The Flatten function is used to transform the list of lists into a single list. The Select function is then used to filter the list of permutations based on the condition that the first and last two letters of each permutation are the same.

letters[words_,n_] := Sort[Flatten[Characters /@ Take[words,n]]];
groupSameQ[g1_, g2_] := Sort /@ Partition[g1, 2] === Sort /@ Partition[g2, 2];
permutations[{a_, b_, c_, d_}] = Union[Permutations[{a, b, c, d}], SameTest -> groupSameQ];
Select[Flatten[permutations /@ 
   Subsets[Union[ToLowerCase/@{"Alabama", "Alaska", "Arizona", "Arkansas", "California", "Colorado", "Connecticut", "Delaware", "Florida", 
      "Georgia", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine", "Maryland", 
      "Massachusetts", "Michigan", "Minnesota", "Mississippi", "Missouri", "Montana", "Nebraska", "Nevada", "New Hampshire", 
      "New Jersey", "New Mexico", "New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma", "Oregon", "Pennsylvania", 
      "Rhode Island", "South Carolina", "South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia", "Washington", 
      "West Virginia", "Wisconsin", "Wyoming"}], {4}], 1], 
 letters[#, 2] === letters[#, -2] &]