A solution
for a tower of height 3
The start. Three discs on the area 1
|
First step: Top disc moves to area 3
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Now we put the medium sized disc to area
2
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The smallest disc goes to area 2. This is
allowed as she above a bigger disc
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Now the disc from the bottom moves to
area 3. No problem - this area is empty
|
The smallest disc jumps to empty area 1
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We are close to our goal. The medium
sized disc moves to area 3. OK, as it is above a bigger
one
|
In the last move we place the smallest
disc to area. Great! We could move a 3 disc tower!
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That was easy, was'n it? Actually, you
might have found a different way to move the tower, but I doubt
that you have one with less moves. If you should have a faster
solution send me an email.
In the next step we will explore a tower
which is a little more complex. But before doing this we should
stop and take a closer look to what we have done (a good idea in
general). Would it be possible to move the tower from area 1 to
area 2 with the same rules? Of course! In the strategy described
above we justa have to replace the word "area 2" with
"area 3" and vice versa! You should try this at home
now.... Done? Okay, we know, it is possible to move a tower of
height 3 from area 1 to area 2.
Well it might get boring, but: Would it be possible to move the
height 3 tower from area 2 to area 3? Give it a try, we will use
all this information (and your experience) on the next page.
Our main results: We may move a tower
of height 3 from area 1 to area 3 according to the restrictions
of the rules. We may also move the same tower from area 1 to area
2 or from area 2 to area 3.
Okay, there is not much left to say
about towers of height 3 and we will explore the next example,
which will give us the key to the 64 disc tower.
...
...
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13-10-2003