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BINGO Mathematics

Edwin Lowe, the son of an orthodox rabbi, introduced the game of BINGO to Americans. He discovered a version of it (called BEANO) at a carnival in Atlanta in December 1929.

Later, Lowe made up 12 different cards and tried it out with with his friends. They loved it...so he produced a version with 24 different cards. Sales took off...

A parish priest at a bankrupt church in Wilkes-Barre (PA) pleaded with Lowe to expand the game to more players...so his church could make enough money to save itself.

Lowe hired a mathematician to create 6000 unique cards...and supposedly the mathematician did so, but "almost went mad."

Consider these facts:

  • A typical BINGO card contain 25 squares arranged in a 5x5 grid
  • The five columns are labeled 'B', 'I', 'N', 'G', and 'O' from left to right
  • The center space is marked "Free" and is considered automatically filled
  • Every other space in the grid contains a number from 1 - 75
  • The 'B' column only contains numbers 1-15, the 'I' column 16-30, the 'N' column 31-45, the 'G' column 46-60, and the 'O' column 61-75
  • When numbers are randomly called (1-75), a player wins the game by covering all of the cells in a row, a column, or a diagonal
Task 1: Investigate why the mathematician had such difficulty. That is, how many unique BINGO cards can be made?

Task 2: What is the greatest number of chips that can be placed on a BINGO board without having a BINGO! (not counting the FREE space)?

Source: Adapted from Ripley's Believe It or Not! Encyclopedia of the Bizarre, 2002, p. 125