Step 1: Clue A1 (New York teams in the corners, Original Six not in column 1) implies that the New York Rangers are A4 and therefore the Buffalo Sabres are H1. You must know the Original Six teams to get this far, they are below:
New York Rangers
Boston Bruins
Montreal Canadiens
Detroit Red Wings
Chicago Blackhawks
Toronto Maple Leafs
Step 2: The first clue of H1 along with the first clue of A4 indicates the Toronto Maple Leafs reside in D4.
Step 3: Clue D4 indicates that the Colorado Avalanche are C2.
Step 4: The first clue of C2 along with the second clue of H1 implies the Dallas Stars are F2. All the relocated teams are as follows:
Dallas Stars (Minnesota North Stars)
Calgary Flames (Atlanta Flames)
Arizona Coyotes (Winnipeg Jets)
New Jersey Devils (Colorado Rockies)
Winnipeg Jets (Atlanta Thrashers)
Colorado Avalanche (Quebec Nordiques)
Carolina Hurricanes (Hartford Whalers)
Step 5: Clue F2 and the first clue of A4 implies that the Montreal Canadiens reside in F4.
Step 6: The second clue of F4 indicates the Minnesota Wild are E1.
Step 7: The second clue of E1 implies that the Carolina Hurricanes belong in H2
Step 8: Clue H2 and the second clue of C2 implies the Edmonton Oilers are A3. In order to get this clue you must know all of Gretzky's fromer teams:
New York Rangers
Edmonton Oilers
Los Angeles Kings
St. Louis Blues
The key to clue H2 is that it say the are al touching each other "individually". That means each of his teams is simultaneously touching all three of his other teams. The only way that is possible is if all of them are in the A3, A4, B3, B4 corner.
Step 9: Clue A3 explains that the San Jose Sharks are B1.
Step 10: Clue B1 inidicates the New Jersey Devils are A2. Clue H2 along with the second clue of A4 indicates the Anaheim Ducks are B2. Now this could be a little tricky, but clue H2 says all of Gretzky's teams are touching one another, inorder for that to be true they must be occupying A3, A4, B3, and B4. This leaves on B2 left for the other California team (Anaheim Ducks).
Step 11: Clue B2 and clue H2 implies the St. Louis Blues are B4. This indicates that the Los Angeles Kings reside in B3. Clue A2 explains that the Vegas Golden Knights belong in F3.
Step 12: Clue F3 implies the Nashville Predators are D3. Clue B3 along with the first clue of A4 indicates the Chicago Blackhawks are C4.
Step 13: Clue D3 explains the Philadelphia Flyers are G3.
Step 14: Clue G3 coupled with the first clue of C2 implies the Pheonix Coyotes belong in D2.
Step 15: Clue D2 indicates the Winnipeg Jets are E2. The first clue of C2 implies that the Calgary Flames are G2 since there is only one spot left in the relcoated teams column.
Step 16: Clue E2 and Clue G2 implies that the Ottawa Senators are C3 and therefore Washington Capitals reside in C1. The first clue of F4 and Clue G2 explains that the only place the Vancouver Canucks can belong is H3. In order to get these teams you must know all the teams that are located in Canada, they are as follows:
Montreal Canadiens
Ottawa Senators
Toronto Maple Leafs
Calgary Flames
Winnipeg Jets
Edmonton Oilers
Vancouver Canucks
Step 17: Clue C1, the first clue of E1, Clue E1, and Clue H3 all indicate the Florida Panthers are F1, while the Tampa Bay Lightning reside in G1.
Step 17: The first clue of A4 and Clue G1 implies that the Detroit Red Wings are G4 and the Boston Bruins are E4. Clue F1 indicates the Pittsburgh Penguins are D1. Finally, the only team left are the Columbus Blue Jackets reside in E3.
HOORAY! The puzzle is complete.