NHL Hockey Puck Puzzle

The NHL Hockey Puck Puzzle is a cylindrical sliding puzzle. It is split into three layers, and around its sides are 24 columns with room for three sliding tiles. The layers can rotate, shifting all the tiles it contains to different columns, and the tiles can slide vertically within a column if there are fewer than 3 tiles in it. When it is solved, most columns contain the logo of an NHL team on the middle tile, and the name of that team split in two parts on the top and bottom tiles. Two of the columns will contain blank tiles, and one column will be completely empty. The columns should be in the order shown in the accompanying leaflet and as indicated by the numbering on the top of the puzzle.

This puzzle is very similar to Whip-It, Varikon, and the Babylon Tower, except that it has three empty slots instead of just one. This makes it rather easy to solve once the intended solution arrangement is known. For an extra challenge, you can try to solve it without rotating the outer layers, using just the middle one.

Here are the teams and logos in the correct order.

Norris Division
1.	2.	3.	4.	5.
Chicago	Detroit	Minnesota	St. Louis	Toronto

Black Hawks	Red Wings	North Stars	Blues	Maple Leafs

Smythe Division
1.	2.	3.	4.	5.
Calgary	Edmonton	Los Angeles	Vancouver	Winnipeg

Flames	Oilers	Kings	Canucks	Jets

Adams Division
1.	2.	3.	4.	5.
Boston	Buffalo	Hartford	Montreal	Quebec

Bruins	Sabres	Whalers	Canadiens	Nordiques

Patrick Division
1.	2.	3.	4.	5.	6.
New Jersey	New York	New York	Philadelphia	Pittsburgh	Washington

Devils	Islanders	Rangers	Flyers	Penguins	Capitals

The NHL Hockey Puck Puzzle was invented by Ali Rahmani, who filed a patent for it on 29 November 1983, CA 1,199,351, which was published 14 January 1986.

The number of positions:

There are 72 tile locations (24 columns on 3 discs), but there are 6 identical blank tiles, 2 identical New York tiles, and 3 empty slots. This gives a total of 72!/(6!2!3!) = 7,087,321,571,398,852,646,009,730,368,666,050,085,738,205,067,673,301,965,720256,361,571,572,336,483,991,814,144,000,000,000,000,000 or approximately 7.1·10⁹⁹ positions. The puzzle is much easier than this number suggests because there are so many empty slots.

Solution:

Put the three blank spots in the same column. I will call this the workspace column.
Choose the column to be solved next, and determine which team and logo should be in that column.
Find one of the pieces that belongs in that column but which has not yet been solved.
Bring that piece to the workspace column:
1. Rotate the disc with that piece to bring it to the workspace column.
2. Slide the piece up or down.
3. Rotate the disc back to where it was.
Determine which spot that piece belongs, and the incorrect piece that is in its spot. Use the same moves as the previous step to bring that incorrect piece into the workspace column.
Insert the correct piece:
1. Slide the correct piece up or down so that it is next to the disc where it belongs.
2. Rotate that disc to bring the empty goal spot to workspace column.
3. Slide the correct piece up or down into the disc where it belongs.
4. Rotate the disc back to where it was.
Get rid of the incorrect piece in the workspace column by using the same moves in the previous step to insert it into the blank spot that is in some other column.
Repeat steps c-g until the chosen column is solved.
Repeat steps b-h until all the columns are solved.

Note that if you are solving a piece that belongs in the middle disc (i.e. a logo piece) then you can combine steps e and f, swapping out one piece for the other.

Jaap's Puzzle Page

NHL Hockey Puck Puzzle

The number of positions:

Solution: