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. **

**Klotski
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.**

**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!**

**aji001.zip
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 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:**

**Mike's and Ed's age.**

**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?**

**Subdivide the region.**

**12 billiard balls**

**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.**

**5 houses****3 glasses****Fork in the Road**

**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.**

**The rational vs. irrational side-length proof of limit of convex polygons makeable with Tangrams.**

**Game Problems:**

**Chess:**

**1 endgame problem**

**Go:**

**1 kikashi problem**

**1 Selective
Perception Problems**

**Count the number of times the letter F appears in the following sentence.**

**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.**