Shuffle list with some conditions

Question

I have a list of elements which can be easily compared using Equals(). I have to shuffle the list, but the shuffle must satisfy one condition:

The i\'th

Answer 1

• permute valid 5 in list, if none unsolvable
• remove permutation from list
• create a cycle graph of that 5
• order the list(remaining list) by count of valid positions in new graph (if you dont do this you can end up with a wrong non solvable, because putting items that can go on more positions increases the possible position count of items with less)
• continue picking items in the list, add items to cycle graph at valid positions
• if there is no valid position in graph or graph cannot be created continue on next
• if graph created revert back to start iteration where graph has been created
• continue creating other graphs
• save all full graphs in a list
• pick a random from that list
• if list is empty unsolvable