Class Chess Tournament

A class of 36 students are expecting to play in the chess tournament held by Math Department. When the schoolmaster arrived he said "Lets start the games but first we must setup all the chess sets". But the schoolmaster did not bring any chess sets.

Instead he brought two mahjong sets and 12 packs of playing cards. The dark and light mahjong tiles are both having 146 solid tiles with (1 5⁄16 in × 1 in × 3⁄4 in) dimensions. 6 packs of available playing cards has dark blue back design while the other 6 packs has red design. (see above). "Any idea how should we make as many chess set as possible out of these?" he asked. Someone suggest that they could use the mahjong tiles as chess pieces and use the cards as chessboard since 4 cards can interlock into 2x2 chessboard. The set chess should be at least readable, playable, simple and there should be regularity of the chess sets. How should the tiles represents the 6 type of chess pieces to make the most number of chess sets for the tournament?

• You should provide the details of exactly what is included in a mahjong set. Commented Jun 17, 2020 at 21:18
• Can we assume an unlimited supply of playing cards? or just the 12 provided in the picture? Commented Jun 17, 2020 at 22:04
• Also, does the fact that there are 36 students imply that we are expected to produce 18 sets? Commented Jun 17, 2020 at 22:09
• @mike details may just complicate this.2) Cards available is just what was brought 12 packs as shown. 3)Not 18 sets thats too many..they can play rounds. Just as much as they can make from above.
– TSLF
Commented Jun 18, 2020 at 0:56
• Lack of detail will complicate this. Relevant details are necessary. I expect that the unidentified extras are not relevant, but the distribution of 144 tiles per set should be explicitly stated. Also, the "best way" to produce the chess sets may be too subjective. This question needs to be improved. Commented Jun 18, 2020 at 2:06

First, each Mahjong set contains the following 146 pieces:

4 each of Bamboo tiles numbered 1-9 (e.g., 4 Bamboos with a 1, 4 Bamboos with a 2, etc.)
4 each of Wheel tiles numbered 1-9
4 each of Wan tiles numbered 1-9
4 each of Wind tiles labeled E, W, S, and N (e.g., 4 East, 4 West, etc.)
4 each of Dragon tiles labeled C, F, and P
1 each of Flower tiles numbered 1-4
1 each of Season tile numbered 1-4 2 extra tiles

Second, a standard playing deck includes 52 cards. Many include 2 jokers.

A very simple strategy that is hinted at in the original question:

Use playing cards to create the board. Use Mahjong tiles as the pieces
12 standard decks of cards results in 324 cards of each color, and 648 total cards
2 standard Mahjong sets results in 146 tiles of each color (counting the 2 extras in each set
Assigning one card per board square results in a maximum of 10 completed chessboards (648/64)
Assigning one Mahjong card per chess piece results in a maximum of 9 completed sets of pieces (146/16)

Now, a system is needed to represent chess pieces with Mahjong tiles. This does not necessarily have to be uniform across all 9 sets

Pawns can simply be the backsides of Mahjong tiles. Thus, they can be any of the 146 tiles
Each Mahjong set (dark and light) must be broken into 9 16-piece sets of chess pieces, 8 of which are pawns
This leaves 9 queens, 9 kings, 18 knights, 18 bishops, and 18 rooks
Designate 9 of 16 Wind tiles as queens
Designate 9 of 12 Dragon tiles as kings
Designate 18 of 36 Wheel tiles as knights
Designate 18 of 36 Bamboo tiles as bishops
Designate the 18 of 36 Wan tiles as rooks

Repeated for each Mahjong set, this allows for some sense of uniformity between the 9 chess sets

This appears to be the maximum number of sets unless the schoolmaster is not too attached to his playing cards

If he is not, you should quarter each card, resulting in 2496 cards Using 1152, we could construct 18 chess boards. These can be any card, regardless of face value
Because each card typically has two identifying symbols (one on the top left and one on the bottom right), we have 96 card pieces of each card number (including royal ace, king, queen, and jack)
Designate 18 kings as chess kings
Designate 18 queens as chess queens
Designate 36 aces as rooks
Designate 36 jacks as bishops
Designate 36 tens as knights
Designate 144 quarter-cards without a symbol as pawns
Cards could be bent slightly in the half and placed as an upside-down V in order to assist in visibility and movement

For each chess game, one side plays with cards and one side plays with Mahjong tiles
This allows for 18 games of chess and accounts for every student

In reality, the remaining pieces might be used to construct additional boards, but that seems unnecessary

• You mentioned 9 sets but also only 16 rooks. What is the source for the other set? Commented Jun 20, 2020 at 2:06
• Youre right about 9sets. All student can play a game in 2 rounds.. so white needs : 9k 9q 18r 18b 18n & 72p (black likewise) . And nice suggestion about sacrificing (cutting) the new cards for 18 sets but not the intended solution.
– TSLF
Commented Jun 20, 2020 at 9:29
• @justhalf thanks for the catch. You can just swaps the wind/wan tiles for rooks/queens
– user69943
Commented Jun 20, 2020 at 21:43

Actually

you can make 10 chess sets using the cards only, even without involving mahjong sets.

The key to the solution is

that you don't need to waste 64 cards for the board. You can use 32 cards to mark the dark squares, and the light squares will be the spaces between them (or vice versa).

So,

The 12 decks provide 12*54=648 cards, so take 32 cards for the pieces (2 kings, 2 queens, 2 jacks (bishops), 2 aces (rooks), 2 tens (knights) and 16 pip cards (pawns) - red suits are for one player and black ones are for the other) from the 10 of 12 decks, and use 320 cards (out of the remaining 328) for making 10 boards.

Representation of 5 types of pieces by its suit was well distributed for dragon Kings, wind Queens,wan Rooks, wheel Knights and bamboo Bishops. The 9 sets by Daniel Choi is shown below with pawns as blanks.

Other possible representation of 6 pieces is by positioning of tiles as noted by Justhalf and applying the faced down pawns above, the regular set looks like: