Something Interesting.

What has this got to do with the meaning of life, the universe and everything?

I will explain.

The above image is a grid consisting of 8 x 8 squares.  This gives a total of 64 squares.  If each square can be either black or white then there are quite a lot of possible arrangements.

The image created could be something interesting like a chess board.  It could be a zig-zag pattern and it could be any alphanumeric character like these:

The grid at the top of this page is randomly allocating the squares each second but if it were showing each and every possible arrangement only once how long would it take to see them all?

How long?

Well there are 18446744073709551616 possible combinations.

If you looked at each arrangement for 1 second it would take

307445734561825860 minutes and 16 seconds or

5124095576030431 hours 0 minutes and 16 seconds or

213503982334601 days, 7 hours, 0 mins & 16 seconds.

Working with 365.25 days per year (accounting for leap years) that is

584542046090 years, 19 hours, 0 mins, & 16 secs.

That's about 584 thousand million years.

There is something interesting about this number of years.

The generally accepted estimated age of planet earth is 4.5 thousand million years.

The rough estimate of the age of the universe is 14 thousand million years.

The time it would take to see all the possible arrangements at a rate of one per second of an 8 x 8 grid of black or white squares is approximately:

  42 times the age of the universe  

The computer Deep Thought in Douglas Adams' series "Hitchhiker's Guide to the Galaxy " came up with the number 42 as an answer to the Ultimate Question of Life, the Universe, and Everything.  Was Deep Thought a 64 bit computer?

Anyway that is an awful lot of time by human standards. And 18446744073709551616 is a very big number. But there are 10 million times more molecules than that in me!