Bingo caller

75-ball bingo, the US game, splits its balls into five columns of fifteen, one per letter of BINGO: B is 1 to 15, I is 16 to 30, N is 31 to 45, G is 46 to 60 and O is 61 to 75. The letter for a ball is its column: column = (ball - 1) ÷ 15, rounded down, plus 1. For 42, (42 - 1) ÷ 15 = 2.73, which rounds down to 2, so 42 is in the third column and is called N-42.

A card is five numbers from each column in a 5 by 5 grid, with a free space in the middle of N. That gives 15 × 14 × 13 × 12 × 11 = 360,360 ways to fill each of B, I, G and O, and 15 × 14 × 13 × 12 = 32,760 ways to fill N, so there are 360,360⁴ × 32,760 = 552,446,474,061,128,648,601,600,000 different cards, about 552 septillion.

The calling order is a shuffle of all 75 balls, so no ball can come up twice and every order is equally likely. To check a claimed bingo, look up each number in the winning line on the board, where the figure in brackets is the call it came out on. Every one must have been called before bingo was shouted.

90-ball bingo is the UK game. Its tickets have 3 rows and 9 columns, five numbers to a row, and the columns hold 1 to 9, 10 to 19 and so on up to 80 to 90. Its numbers are called without letters, and a game is usually played for one line, then two lines, then a full house of all fifteen.