<s>[INST] This challenge involves arranging a list of words into an order that satisfies a given set of rules. The rules are:

• The list is a cyclical list, i.e., the last word can be matched with the first word.
• Each word must be matched with a word that does not contain any of the letters of the previous word.
• The rules are case insensitive, and hyphens, spaces are ignored when matching letters.
 
Here is an example of a list of words: ["apple", "banana", "cherry", "date", "elderberry", "fig"]

Please let's get the words to be arranged with a correct order and return it as a Python list.

Here is an implementation code for this problem and I had a problem with making the list as a cyclical:
```
           words = ["apple", "banana", "cherry", "date", "elderberry", "fig"]
       words_lower = [word.lower().replace('-', '').replace(' ', '') for word in words]
       word_dict = {word: set(word) for word in words_lower}
       for word1 in words_lower:
           for word2 in words_lower:
               if word1 == word2:
                   continue
               if not word_dict[word2].isdisjoint(word_dict[word1]):
                   word_dict[word1].add(word2)
       for i in range(len(words)):
           for j in range(i+1, len(words)):
               if words_lower[i] in word_dict[words_lower[j]]:
                   word_dict[words_lower[i]].remove(words_lower[j])
       result = []
       while words:
           for i in range(len(words)):
               for j in range(len(words)):
                   if words_lower[i] not in word_dict[words_lower[j]]:
                       result.append(words[i])
                       words = words[1:] if i == 0 else words[:i] + words[i+1:]
                       words_lower = words_lower[1:] if i == 0 else words_lower[:i] + words_lower[i+1:]
                       word_dict = {key: value.difference({words_lower[i]}) for key, value in word_dict.items()}
                       break
               else:
                   continue
               break
           else:
               raise Exception('No solution exists')
       print(result)
```
Now I got issue to check the word in the end of list can match with the first word after arranging, since the list is cyclical. I need a solution with valid code representation for the issue and the corresponding insights.[/INST]