APL routines for US Bingo

APL routines for US Bingo

The following is a niladic function called AplPickEm
used to randomly generate a strip of three 5x5 US Bingo
cards with all 75 numbers.

This was tested using Dyalog APL 12.1.

N.B. The index origin ⎕IO is 1

∇ AplPickEm;X;A;B;C
⍝ APL program to randomly generate three 75-ball Bingo cards
X←75 ⍴ X←⍉5 15 ⍴ (15?15),(15+15?15),(30+15?15),(45+15?15),60+15?15
A← 6 5 ⍴ 'BINGO', 25 ↑ X
A[4;3]← 'X' ⍝ Blot-out the "FREE" space
A ⍝ Print first card
⎕←⍳0 ⍝ Newline
B← 6 5 ⍴ 'BINGO', 25 ↑ 25 ↓ X
B[4;3]← 'X'
B
⎕←⍳0 ⍝ Newline
C← 6 5 ⍴ 'BINGO', 50 ↓ X
C[4;3]← 'X'
C
∇

The function is run by entering it's name:

AplPickEm

It produces output like the following:

B  I  N  G  O
6 18 42 48 75
7 19 41 52 67
8 24  X 55 66
9 29 34 51 72
4 28 33 59 68

 B  I  N  G  O
 3 26 38 47 73
 2 20 39 60 74
10 25  X 46 71
 1 16 37 53 70
14 22 44 54 65

 B  I  N  G  O
 5 27 36 57 69
11 17 40 50 64
15 21  X 49 61
13 23 35 58 62
12 30 45 56 63

Here is the code to draw the numbers 1-75 at random...

⍝ One-time initialization of global variables
∇ Init
N ← 0,15×⍳5
L ← 'BINGO'
⍝ Map numbers 1-75 to letters 'BINGO'
MAP←((⍳75)∘.≥1+5↑N)^(⍳75)∘.≤1↓N
∇

⍝ Shuffle the deck of Bingo calling cards
∇ Shuffle
DECK ← 75?75
∇

⍝ Draw the next Bingo calling card from the deck
∇ Draw;C
⍝ Pick a calling card C from the deck
C ← 1↑DECK
DECK ← 1↓DECK
⍝ Map C to letters 'BINGO'
C ← ((,MAP[C;]) / L), ' ', C
⍝ Call the result
C
∇

⍝ Play a game until someone shouts "BINGO!"
      Init
      Shuffle
      Draw
B  10
      Draw
G  57
      Draw
N  36
...

⍝ Finally, the code to compute the number of all possible Bingo cards
f←{(!⍵)×⍵!15}
(f 4)×(f 5)*4

5.524464741E26