# 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.
ChicagoDetroitMinnesotaSt. LouisToronto
Black HawksRed WingsNorth StarsBluesMaple Leafs
Smythe Division
1.2.3.4.5.
CalgaryEdmontonLos AngelesVancouverWinnipeg
FlamesOilersKingsCanucksJets
1.2.3.4.5.
BostonBuffaloHartfordMontrealQuebec
Patrick Division
1.2.3.4.5.6.
DevilsIslandersRangersFlyersPenguinsCapitals

## 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:

1. Put the three blank spots in the same column. I will call this the workspace column.
2. Choose the column to be solved next, and determine which team and logo should be in that column.
3. Find one of the pieces that belongs in that column but which has not yet been solved.
4. 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.
5. 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.
6. 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.
7. 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.
8. Repeat steps c-g until the chosen column is solved.
9. 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.