Aji's Math and Puzzels Page

Paragraph's in this color are new additions/modifications to this page.

Click on Rubik's Cube to go to that page.

Fermat's Last Theorem:

The Mathematics of Fermat's Last Theorem

For n = 2 we know that the equation not only has a solution but an infinate number of solutions.  x = 3, y = 4 and z = 5 and any positve interger multiple of these.
It even has an infinate number of solutions not allowing for multiples:
x = 5, y = 12, z = 13 being one of these.  But the proof of this has eluded civilization for 300 years even though Fermat said that the margin of his book was too small to show what he claimed was a proof.  It seems almost impossible Fermat ever did have a proof as Wile's proof draws on 5 different areas of modern number theory.  Click ENTER once there.

This is an ancient Polish puzzel game that was included in a free games disk by Verbatim.  After Rubik's cube I enjoyed the most difficult puzzel Sunshine which I now have under 1850 steps in a Windows Recorder file for both Win 3.x and Win 95.  I challenge anyone to improve on my solution by more than 10 steps.  It is included in the file aji001.zip.
(Such bravado!  New links here to be provided shortly will make my challenge look silly.)

A bone is thrown over the fence from a dog.  The dog tries to get to the bone by penetrating the fence which fails.  All the dog needed to do was to go away from the goal to an opening in the fence to get to the other side and then the bone.  However he failed since what appeared to her was the shortest way to the bone only yielded [sic? i before e except after c?] failure.  My approach to Sunshine was to increase the degrees of freedom by moving 2 of the large squarges diagonally opposite.  However there is a way to get through those squares by 'going through the fence!'

Klotski is now available as freeware from Surf Madison but I don't have time to retrieve the link but a Yahoo! search will find it.  Actually if you cant wait look up Bricks by Andreas Rottler.  I just looked up the link to Bricks homepage: Bricks Game Home Page www.bricks-game.de www.rottus.de

This is a better way to play Klotski puzzels that tracks your moves!

This has more puzzels and other stuff but I don't know how to set up an FTP link in my pages yet so you have to E-mail me at   [email protected]  to request it.
 This will be superceded soon but I don't need an FTP link for you to get it.  Just click the following link to download it: AJI001.ZIP

This is from an older web site and in time I will post this on this page.

New Additions (in progress this week Feb. 17, 2005):

Math Problems:

The sum of Mike's and Ed's ages is 44 years.
Mike is twice as old as Ed was when Mike was half as old as
Ed will be when Ed is three times as old as Mike was when
Mike was three times as old as Ed.

How old is Mike?

You have 12 billiard balls (labeled A through L) all weighing the
same except for one.  Using a balance for only three weighings tell
which has the unique weight and whether it is heavier or lighter
than the other eleven.

This must be shown for all possible cases.

Your traveling down a road that forks to the left and the right.  One branch is the road to everything good; the other to everything bad. At the start of each branch a man stands.  One man is good and tells the truth 100% of the time.  The other man is bad and tells lies 100% of the time.  The men know nothing of each other.  You do not know which is which and the good man does not necessarily stand on the good road.  You have only one question to ask to only one of the men that will have a yes/no answer.  What question should you ask and based on the answer do you go down his road? This must be shown for all possible four cases.

Game Problems:



1 Selective Perception Problems

The solutions will NOT be posted here. You must E-mail me for them AFTER trying them.  Then I will provide you with the secret links.

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