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Anyone up for a Game of Life?

John Conway
I just read a nice tribute article for John Conway - it set me pondering the ways humans think.  The photograph makes me think John could be Logan's (Wolverine) father.

John Conway Solved Mathematical Problems With His Bare Hands

I wonder if Conway had a unique thinking process - it appears so.  Yet he was able to explain many problems and solutions quite elegantly.  The article details a few of his elegant solutions.

The Game of Life
You have most likely heard of his Game of Life.
The game of life came up recently in another article I was reading about Physics - Stephen Wolfram describes (for the layperson) a system that may have an ability to describe the fundamental theory of physics many have been searching for.  I question if we will actually know it - when and if - we actually see it.

Finally We May Have a Path to the Fundamental Theory of Physics…  and It’s Beautiful


So ignore all this background noise for a moment and ponder this ...  riddle, given to me by my sister-in-law Shannon.  
In a new hotel containing 100 rooms, Tom was hired to paint the numbers from 1-100 on the doors. How many times will Tom have to paint the number 8?
Ok, I'm less interested in the answer - I'm more interested in the methods people use to come up with their answers - either right or wrong.  I wonder - could a mathematician such as Conway describe the set of methods used by humans to create a solution (either right or wrong).  And would one of those meta-methods prove more useful in many situations?  The article's title about Conway suggests one method - do it by hand.  I take this to mean - write out the numbers from 1 -100 that contains an eight.  OK, that is one method... what's another method?  I've come up with 3 methods.  Two that result in correct solutions and one that arrives at an incorrect solution. 

So why is this simple problem a riddle?  I think it is because humans will tend to use the method that results in many people having an incorrect solution.  Now, why is that solution preferred by so many people?  Is it because the solution is easy - takes little energy - does not have any verification steps and results in a reasonable face value answer. 

Yes, humans were made to be lazy... it's one of our best qualities - when used well.

See Also:
Study finds we often know the best decision, but choose another path instead - by John Anderer
Another riddle:  How many Ones will Tom paint, and how many Zeros?

The Trouble With Stephen Wolfram’s New 'Fundamental Theory of Physics' - Ryan F. Mandelbaum

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