Random Number Generation

March 9, 2012 at 12:01 am Leave a comment

While playing Nurikabe, my sons completed the following puzzle:

Nurikabe - RNG

The puzzle itself isn’t very interesting, but did you notice the Puzzle ID? Exactly 1,000,000. The boys thought this was pretty cool, and I did, too. Yeah, yeah, I know, the occurrence of 1,000,000 shouldn’t impress me more than the appearance of, say, 8,398,176 or 3,763,985. But there are just under 10,000,000 unique 5 × 5 puzzles on the site, and only nine of them contain six 0′s. How lucky were we to get that random number?

Generating random numbers can be a difficult proposition, especially for a computer. This article from WIRED magazine — which describes a pattern that inadvertently appeared on lottery tickets, making it possible to predict winning tickets before they were scratched — shows how difficult it can be to generate numbers that appear to be random. (The article really is worth a read, especially for math geeks. Truth be known, WIRED is the only magazine that I read cover-to-cover every month.)

Robert Coveyou, a mathematician who worked on the Manhattan project, was an expert in pseudo-random number generators. He is most famously remembered for the following quote:

The generation of random numbers is too important to be left to chance.

Of course, Randall Munroe at xkcd has a foolproof method for generating a random number:

I would hate for you to need a random number and then have difficulty generating one. I’m here to help, so I present the…

MJ4MF Random Number Generator (PDF)

Creating the MJ4MF RNG is quite simple. Just follow these steps:

  1. Download and print the PDF from the link above.
  2. Cut out all six squares, one for each number 1-6.
  3. For each square, make two folds: first, fold the paper to the center vertically; then, fold the paper to the center horizontally. The result of these two folds is shown, below left.
  4. When all six pieces are folded, interlace them to form a cube. This is shown, below middle. The assembled cube is shown, below right.

RNG Assembly

Finally, a joke about random numbers.

A student is asked for the probability that a random number chosen between 0 and 1 will be greater than 2/3. The student answers 1/3. The teacher says, “Great! Can you explain to the class how you arrived at your answer?” The student says, “There are three possibilities: the number is either less than, equal to, or greater than 2/3, so the probability is 1/3!”

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About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.


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